Chapter 6: Circuits Flashcards
By historical convention, which direction is current flow?
Because of historical conventions, current is considered the flow of positive charge.
Even though only negative charges are actually moving.
Any conductive substance may act as a medium through which current can pass.
What is metallic conductivity what is electrolytic conductivity?
Conductivity can be divided into two categories: metallic and electrolytic conductivity.
Metallic conductivity is seen in solid metals and molten forms of some salts.
Electrolyte conductivity is seen in solutions.
What is conductance? What is the SI unit for conductance?
Conduction is the reciprocal of resistance. The SI unit for conductance is the siemens (S), sometimes siemens per meter (S/m).
Recall where metals are found on the periodic table. Relate this to ionization energy and thus metals tendency with electrons.
Remember that the metals are found on the left side of the periodic table. These are at the atoms with the lowest ionization energies; thus it is easiest for these atoms to lose electrons. Due to this weak hold (due to low ionization energies) electrons are free to move around in the metal, conducting electrical charges.
What is an electrical conductor? What material makes good electrical conductors?
An electrical conductor allow free flow of electric charge within them. Metals can easily lose one or more of their outer electrons, which are then free to move around in the larger collection of metal atoms, this being good electrical and thermal conductors.
How are metallic bonds visualized?
Metallic bonds are often visualized as a sea of electrons flowing over and past a rigid lattice of metal cations.
What does the strength of electrolytic conductivity rely on?
The strength of electrolytic conductivity relies on the concentration of solution.
For example, distilled deionized water has such a low ion concentration that it may be considered an insulator.
Because concentration and conductivity are directly related, this method is often used to determine ionic concentrations in solutions, such as blood.
What is current? How do we calculate the magnitude of current? What is the SI unit of current?
Current is the flow of charge between two points at different electrical potentials connected by a conductor.
The magnitude of current is the amount of charge passing through a conductor per unit time.
The unit of current is the ampere and one ampere equals one coulomb per second.
There are two patterns of current flow. What are they?
Direct current (DC) in which the charge flows in one direction only (household batteries)
Alternating current (AC) in which the flow changes direction periodically (long distance power, such as power to a home)
Charge is transmitted by a flow of electrons in a conductor. Regarding electrical potential, which direction will an electron move?
Because electrons are negatively charged, they move from a point of lower electrical potential to a point of higher electrical potential (and in doing so reduce their electrical potential energy).
What do we call voltage when no charge is moving between two terminals of a cell that are at different potential values?
When no charge is moving between the two terminals of a cell that are at different potential values, the voltage is called the electromotive force (emf).
Is electromotive force an actual force?
Electromotive force is not actually a force. It is a potential difference (voltage) and as such as units of volts (Joules/Coulomb), not Newtons.
Currents (and circuits in general) are governed by the laws of conservation. How so?
Charge an energy must be fully accounted for at all times and can be neither created nor destroyed.
What is Kirchhoff’s junction rule?
Kirchhoff’s junction rule states that at any point or junction in a circuit, the sum of currents directed into that point equals the sum of current directed away from that point. This is an expression of conservation of electrical charge and can be expressed as:
Example Kirchhoff’s junction rule page 214
What is Kirchhoff’s loop law?
Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops.
This is a consequence of the conservation of energy. All the electrical energy supplied by a source gets fully used up by the other elements within that loop. No energy appears, no energy appears that cannot be accounted for.
This law is in terms of voltage (joules/coulomb), not just energy (joules).
MCAT concept check 6.1 Current page 215 question 1
Also conductivity
Current is the movement of positive charge through a conductive material overtime and is given in Amperes (A = coulomb per second).
Voltage is a potential difference between two points and is given in volts (V = J/C).
Electromotive force refers to the potential difference of the voltage source for a current, usually a battery, and is given in volts (V = J/C)
Conductivity is the reciprocal of resistance and is a measure of permissiveness to current flow and it is measured in siemens (S, sometimes S/m)
MCAT concept check 6.1 Current page 215 question 2
The sodium chloride solution likely has a higher conductivity because it is a salt and will increase the ion content of water. Glucose does not dissociate, and therefore it has a near zero impact on conductivity (effectively no net charge in water).
MCAT concept check 6.1 Current page 215 question 3 and 4
True. This is a statement of Kirchhoff junction rule. Current in = Current out
False. While the voltage sources and voltage drops are equal in any closed loop, this is not necessarily true for the entire circuit. For example, a 9 V battery that powers 10 lightbulbs in parallel has a 9 V voltage source and a 9 V drop across each lightbulb, a total of 90 V of drop across all of the lightbulbs combined.
What is resistance?
Resistance is the opposition within any material to the movement and flow of charge. Electrical resistance can be thought of like friction, air resistance, or viscous drag: in all of these cases, motion is being opposed.
Materials that offer almost no resistance are called conductors, and those materials that offer very high resistance are called insulators.
What is a resistor?
Conductive materials that offer amounts of resistance between conductors and insulators are called resistors.
A resistor is an electrical component that limits or regulates the flow of electrical current in an electronic circuit.
The resistance of a resistor is dependent upon certain characteristics of the resistor. What are these characteristics (
Resistivity, length, cross-sectional area, and temperature are the characteristics of a resistor that characterize its resistance.
What is the equation for resistance?
What is resistivity?
The number that characterizes the intrinsic resistance to current flow in a material is called resistivity. The SI unit for resistivity is the ohm-meter.
Derive the units of resistivity using the equation for resistance.
What happens to resistance when length is increased. How does this factor scale?
According to the resistance equation, the resistance of a resistor is directly proportional to its length. This factor scales linearly: if a resistor doubles its length, it will also double its resistance.
How does cross-sectional area impact resistance? What is a conduction pathway?
The equation for resistance also demonstrates an inverse proportionality between resistance and the cross-sectional area of a resistor.
If a resistor cross-sectional area is doubled, its resistance will be cut in half.
An increase in cross-sectional area increases the numbers of pathways through the resistor, called conduction pathways.
Why does increasing cross-sectional area decrease resistance?
An increase in cross-section area increases the number of pathways through the resistor called conduction pathways. The wider resistor, the more current that can flow.
This is analogous to a river, where the wider the river, the less resistance there is to water flow.
How does temperature impact resistance?
Most conductors have greater resistance and higher temperature. This is due to increase the thermal oscillation of the atoms in the conductive material, which produce a greater resistance to electron flow.
The voltage drop between any two points in a circuit can be calculated according to ohms law. What is the equation for ohms law?
Describe ohms law
Ohms law relates resultant energy loss as voltage drop due to resistance.
We can think of resistance as a non-conservative force like friction in that energy is lost through non-conservative forces. The resultant energy loss is called voltage drop.
Voltage can be harnessed to do work through resistance.
Book description of Ohms law
Ohms law is the basic law of electricity because it states that for a given magnitude of resistance, the voltage drop across the resistor will be proportional to the magnitude of the current. Likewise, for a given resistance, the magnitude of the current will be proportional to the magnitude of the emf (voltage) and impressed upon the circuit.
The equation applies to a single resistor within a circuit, to any part of the circuit, or to an entire circuit (provided one can calculate the equivalent resistance from all the resistors in the circuit).
As current moves through a set of resistors in a circuit, the voltage drop some amount in each resistor; the current (or some of currents for a divided circuit) is constant. No charges gained or lost through a resistor; thus, if resistors are connected in series, all of the current must pass through each resistor.
Is charge lost through resistors?
No charge is gained or lost through a resistor. If resistors are connected in series, all of the current must pass through each resistor.
What is electrical current?
Electrical current is the flow of charge between two points at different electrical potentials connected by a conductor, such as a copper wire.
Magnitude of electrical current (I) is the amount of charge (Q) passing through the conductor per unit time (deltat)
Conductive materials, and even the very sources of emf (voltage), have a measure of internal resistance. What is internal resistance and what is the equation for voltage given internal resistance?
Conductors act as weak resistors and offer some magnitude of resistance that causes a drop in electrical potential (voltage). As a result of internal resistance, the voltage supplied to a conduit is reduced from its theoretical emf value by some small amount given by the equation:
What is power? What are the units of power?
Power is the rate at which energy is transformed or transferred. The unit for power is the watt (J/s) and is work per time, or change of energy per time.
Express power as an equation. The purpose of this is to understand what power represents.
Bonus. What is work? What are three equations for work?
Given that power is change of energy per time (watt), and work is change in energy (joule), power can be expressed as:
What is the power of a resistor?
The rate at which energy is dissipated by a resistor is known as the power of the resistor.
The “power of a resistor” refers to the maximum amount of electrical power a resistor can dissipate without being damaged, measured in watts (W) and often called the “power rating” of the resistor.
The rate at which energy is dissipated by a resistor is known as the power of the resistor. What is the equation for the power of a resistor?
Three equations for power of a resistor can be interconverted using ohms law. What are these three equation?
Remember these equations. There are three equations for the power of a resistor. What are those three equations?
Power, current, and voltage are all related. How so?
What is a superconductor?
How can power companies manipulate current and voltage while maintaining the same power?
Power is the product of voltage and current (P=IV). We can manipulate either current and voltage while maintaining the same power (watt = energy per time).
We can increase the current, which results in a decrease in voltage.
We can increase the voltage, which results in a decrease in current.
Power companies use high voltage lines, which allow them to carry a smaller current, thus decreasing the amount of energy lost from the system.
Resistors can be connected into a circuit in one of two ways: series and parallel. What is the difference?
Resistors in series are resistors in which all current must pass sequentially through each resistor connected in a linear arrangement.
Resistors in parallel are resistors in which the current will divide to pass through resistors separately.
For resistors connected in series, speak about the current and voltage.
For resistors connected in series, the current has no choice, but to travel through each resistor in order to return to the cell.
As the electrons flow through each resistor, energy is dissipated, and there is a voltage drop associated with each resistor. The voltage drops are additive. Vs=V1+V2+V3…+Vn
Because V=IR, we can also see that the resistances of resistors in series are also additive:
Rs=R1+R2+R3…+Rn
The set of resistors wired in series can be treated as a single resistor with a resistance equal to the sum of the individual resistances, termed the equivalent or resultant resistance. Note that Rs will always increase as more resistors are added.
What is equivalent or resultant resistance?
The set of resistors wired in series can be treated as a single resistor with a resistance equal to the sum of the individual resistances. This is known as the equivalent or resultant resistance.
Note that this will always increase as more resistors are added.
Once you know the current of the whole circuit, how do you solve for the voltage drop across each resistor?
When there is only one path for the current to take, the current will be the same at every point in the line, including through every resistor.
Once you know the current of the whole circuit you can use V=IR to solve for the voltage drop across each resistor (assuming you know the resistance of the resistors).
Series circuit example page 220
Parallel resistor example page 223
Consider two equal resistors wired and parallel. What is the equivalent resistance of the set up?
The equivalent resistance of the set up where R1=R2 which gives us Rp=R/2
We can see that the total resistance is have by wiring, two identical resistors in parallel. More generally, when an identical resistors are wired in parallel, the total resistance is given by R/n.
When n identical resistors are wired in parallel, what will the total resistance be? Will the voltage across each of the parallel resistors be equal? Well, the current flowing through each of the resistors be equal?
Page 223
When n identical resistors are wired in parallel, the total resistance is given by R/n.
The voltage across each of the parallel resistors is equal.
And for equal resistance, the current flowing through each of the resistors is also equal (Itotal/n runs through each resistor).
MCAT concept check resistance 6.2 page 224 question 1
How does adding a removing a resistor change the total resistance of a circuit with resistors in series? Parallel?
Total resistance increases when adding a resistor to resistors in series, total resistance decreases when removing a resistor from resistors in series.
Total resistance decreases when adding a resistor to resistors in parallel, total resistance increases when removing a resistor from resistors in series. It
MCAT concept check resistance 6.2 page 224 question 2
Resistivity, length, cross-sectional area and temperature determine the resistance of a resistor.
Increase Resistivity increases resistance,
Increase Length increases resistance,
Increase cross-sectional area decreases resistance,
Increased temperature increase resistance
MCAT concept check resistance 6.2 page 224 question 3
How does power relate to current, voltage, and resistance?
MCAT concept check resistance 6.2 page 224 question 4
True or false: the internal resistance of a battery will lower the amount of current it can provide.
True. The internal resistance will lower the available voltage for the circuit. Lowering the available voltage will also lower current for any given resistance.
MCAT concept check resistance 6.2 page 224 question 5
All current must travel through the first resistor, regardless of its resistance. The ratio of resistance for R2:R3 is 1:3, the ratio of current passing through them will be 3:1. 3/4 of the current will pass through R2, 1/4 of the current will pass through R3.
How do electric circuits work? Use the words: redox reaction, energy, flow of electrons, kinetic energy, emf, current, resistor.
In electric circuits, energy is supplied by the cell that houses a spontaneous redox reaction, which once allowed to proceed, generates a flow of electrons. And these electrons, which have electrical potential energy, convert that energy into kinetic energy as they move around the circuit, driven by the emf of the cell. Emf is not a force, but is better thought of as a pressure to move, exerted by the cell on the electrons. Current delivers energy to the various resistors, which convert this energy to some other form, depending on the particular configuration of the resistor.
What are capacitors? What is a relevant example of a capacitor (for medical use)?
Capacitors are characterized by their ability to hold charge at a particular voltage.
The defibrillator is an excellent example of a capacitor. While a defibrillator is charging, a high-pitched electronic tone sounds as electrons buildup on the capacitor. When the defibrillator is fully charged, that charge can be released in one surge of power.
The clouds in the air during a lightning storm also act as a capacitor, which the charge buildup between them eventually discharging as a bolt of lightning.
What type of capacitor does the MCAT particularly focus on?
The MCAT focuses on a particular type of capacitor, called parallel plate, capacitor, and all of our discussion will center on capacitors of this type.
What is capacitance of a capacitor defined as?
Capacitance of a capacitor is defined as the ratio of the magnitude of the charge stored on one plate to the potential difference (voltage) across the capacitor.
Therefore, if a voltage V is applied across the plates of a capacitor and a charge Q collects on it, then the capacitance is given by the following equation:
What is the equation for capacitance? What is the unit for capacitance?
In order to understand the magnitude of one farad:
What is the farad capacitance of a defibrillator? A lightning cloud?
Capacitance of a defibrillator: 40-80 microfarad (0.00006 F)
Logging cloud: a few farad
Is farad the same as the faraday constant?
No. One farad is one C/V.
Faraday constant is 10^5 C/mol e-
For the simple case of a parallel plate capacitor, what is the equation for capacitance?
What is the equation for a uniform electric field between the plates with parallel field vectors?
What is the equation for potential energy stored in a capacitor?
What is a dielectric material?
Dielectric material is just another way of saying insulation.
Describe a parallel two plate capacitor and the capacitance of that capacitor.
Two electrically neutral metal plates are connected to a voltage source, positive charge builds up on the plate connected to the positive (higher potential) terminal, negative charge builds up on the plate connected to the negative (lower potential) terminal.
The two plate system is a capacitor because it can store a particular amount of charge at a particular voltage.
The capacitance of a capacitor is defined as the ratio of the magnitude of the charge stored on one plate to the potential difference (voltage) across the capacitor.
Voltage V is applied across the plates of a capacitor in charge Q collects on it (positive Q on the positive plate and negative Q on the negative plate), then the capacitance is given by C=C/V
The separation of charges between two parallel plates set up a uniform electric field between the plates with parallel field vectors. How can we calculate the magnitude of the uniform electric field created? Which way will the uniform electric field be pointing?
The electric field vector points from the positive (higher potential) toward the negative (lower potential).
Regardless of the particular geometry of a capacitor (parallel or otherwise) the function of a capacitor is to store an amount of energy in the form of charge separation at a particular voltage. How can we calculate the potential energy stored in a capacitor?
We can derive the equation for a uniform electric field between plates with parallel field vectors from the other fundamental electrostatic equations shown in the image. Do that.
Use image if needed.
What happens when a dielectric material such as air, glass, plastic, ceramic, is introduced between the plates of a capacitor?
When a dielectric material is introduced between the plates of a capacitor, and increases the capacitance by a factor called the dielectric constant.
What is the dielectric constant of a material? What is the dialect constant of a vacuum?
The dielectric constant of a material is a measure of its insulating ability, and a vacuum has a dielectric constant of one, by definition.
What can be inferred about the insulating ability of a dielectric material of seven versus a dialectic material of two?
The dielectric material of seven will be a far better insulator than the material with a dielectric material of two.
How do we calculate the capacitance of a parallel plate capacitor due to a dielectric material?
The capacitance of a parallel plate capacitor will increase due to the presence of a dielectric material by a factor of the dielectric constant of the material. When a dielectric material is introduced into an isolated capacitor, the increase in capacitance arises from a decrease in voltage.
When a dielectric material is placed in a charge capacitor with a circuit, the charge on the capacitor increases. What must happen if capacitance is increased? What causes the increase in capacitance?
The increase in capacitance is due to the present of the dielectric material, thus the capacitance of the capacitor increases by a factor of the dialect constant. Thus, when a dielectric material is introduced into a circuit capacitor, the increase in capacitance arises from an increase in stored charge (recalling that capacitance equals charge per voltage).
Charge, capacitance, and voltage of a capacitor example page 228
Charge capacitance and voltage of a capacitor with a dielectric material example page 228
When capacitors are connected in series, what happens to the total capacitance of the series?
When capacitors are connected in series, the total capacitance decreases in similar fashion to the decrease in resistance seen in parallel resistors.
Functionally, a group of capacitors in series acts like one equivalent capacitor with a much larger distance between its plates. In fact, with the distance equal to those of each of the series capacitors added together. This increase in distance means a smaller capacitance.
Note that for capacitors in series, the total voltage is the sum of the individual voltages, just like resistors in series.
When capacitors are wired in parallel, what will the resultant capacitance of the system equal?
When capacitors are wired in parallel, they will produce a result in capacitance that is equal to the sum of the individual capacitances.
Just as we saw with resistors in parallel, the voltage across each parallel capacitor is the same and is equal to the voltage across the source.
MCAT concept check capacitors 6.3 page 230 question 1
Assuming the plates are attracted by a conducting material, how does a capacitor behave after the voltage source has been removed from a circuit?
The capacitor discharges, providing a current in the opposite direction of the initial current.
MCAT concept check capacitors 6.3 page 230 question 2
How does a dielectric material impact capacitance? Voltage? Charge?
A dielectric material will always increase capacitance.
If the capacitor is isolated, its voltage will decrease when a dielectric material is introduced. If a capacitor is in a circuit, its voltage is constant because it is dictated by the voltage source.
If a capacitor is isolated, the stored charge will remain constant because there is no additional source of charge. If the capacitor is in a circuit, the stored charge will increase.
MCAT concept check capacitors 6.3 page 230 question 3
How does adding or removing a capacitor change the total capacitance of a circuit with capacitors in series? In parallel?
Adding a capacitor in series decreases the total capacitance of a circuit; removing one in series increases the total capacitance in the circuit.
Adding a capacitor in parallel, increases the total capacitance, removing a capacitor in parallel decreases the total capacitance.
MCAT concept check capacitors 6.3 page 230 question 4
What physical qualities contribute to the capacitance of a capacitor?
Surface area, distance, and dialect constant all contribute to the capacitance of a capacitor.
What is an ammeter? What property does an ideal ammeter possess? Why?
An ammeter is used to measure current at some point within a circuit. Using an ammeter requires a circuit to be on, or the current will be 0 A.
Ammeters must have extremely low resistance otherwise it will change circuit mathematics when it is inserted into the circuit.
IDEAL IN METERS HAVE ZERO RESISTANCE AND NO VOLTAGE DROP ACROSS THEMSELVES.
What is a voltmeter? What property does an ideal voltmeter have? Why?
Voltmeters are used to measure the voltage drop across two points in a circuit. They are wired in parallel to these two points. Because the goal with any meter is to minimize its impact on the rest of the circuit and voltmeter are wired in parallel and ideal voltmeter has infinite resistance.
What is an ohmmeter?
An ohmmeter does not require a circuit to be active. Ohmmeters will often have their own battery of known voltage and then function as ammeters through another point in the circuit. Because only one circuit element is being analyzed, ohms law can be used to calculate resistance by knowing the meters voltage and the current created through another point in the circuit.
MCAT concept check Meters 6.4 page 232 question 1
MCAT concept check Meters 6.4 page 232 question 2
True or false: a voltmeter and an ammeter should not be placed in the same circuit.
False. Voltmeters and ammeters are designed to have minimum impact on a circuit; thus, they can be used together.
Relevant equations and relationships from chapter 6 circuits
Circuits MCAT mastery page 206 question 1
Electric current is defined as charge flow, or in mathematical terms: charge transferred per time.
Circuits MCAT mastery page 206 question 2
To measure the current at any point in a circuit, an ammeter should be placed in series. Placed in parallel, a new path for current would be created, so the Measure value would not be reflective of actual current in the circuit.
The ideal ammeter should have zero resistance so that it has no effect on the current of the circuit.
Circuits MCAT mastery page 206 question 3
This is a proportionality problem. We know that resistance equals resistivity times length divided by area. If lengthen area are held constant, we know that resistance is directly proportional to resistivity. This means that the ratio of resistivity will equal the ratio of resistance.
Circuits MCAT mastery page 206 question 4
Circuits MCAT mastery page 206 question 5
Circuits MCAT mastery page 206 question 6
The trick to this one is seeing three resistors in parallel. (R1), (R234), and (R56)
Start by noticing our three and four are in parallel, and calculate.
Take that resistance from three and four, and notice it is in series with two.
Five and six are in series.
Now we can add together three resistors in parallel.
Book description:
Simplify the circuit bit by bit. Noticed that R3 and R4 are in parallel with each other and are in series with R2. Similarly, R5 and R6 are in series. If we determine the total resistance in each branch, we will be left with three branches in parallel. To start, find the total resistance in the middle branch. Next take a look at the total resistance in the bottom branch. The circuit can now be viewed as three resistors in parallel, each providing a resistance of 20 ohms.
Circuits MCAT mastery page 206 question 7
Circuits MCAT mastery page 206 question 8
This problem gives us a circuit with the voltage source with some parallel resistors and resistors in series.
First thing we should do is solve for the current given by V=IR….. I=V/R.
Once we have the current, we can determine the voltage drop across the 1/2 resistor.
Kirchhoffs loop law tells us that the sum of voltage sources will always be equal to the sum of voltage drops.
Circuits MCAT mastery page 206 question 9
Our initial guest was A. This is a good question to recognize proportionality.
If you double the area capacitance increases by a factor of two because area is in the numerator of the equation (and it makes intuitive sense)
If you half the distance between them it will also double the capacitance. We need to recognize that dividing by half is like multiplying by two.
Thinking intuitively of what we know about capacitors: larger area of overlapping plates and smaller distance between them will increase capacitance.
Circuits MCAT mastery page 206 question 10
Identify that we need to solve for Q.
C=Q/V and the given equation for energy stored in a capacitor. Combining these two equations gives us a way to solve for Q given voltage and stored energy.
Circuits MCAT mastery page 206 question 11
To solve this question, we need to define what power is. Power is energy dissipated per time. Therefore, energy is the product of power and time.
Secondly, we need to know the equation for the power of a resistor: P=IV. We don’t have voltage, but we know voltage equals the product of current and resistance. This allows to calculate power given current and resistance.
Circuits MCAT mastery page 206 question 12
Circuits MCAT mastery page 206 question 13
We first tried to solve this by solving for capacitance of a capacitor and its relationship to permissive of free space, area of plates, and distance between plates. This is not the way to solve this problem.
This problem is asking about the electric field of a capacitor. The electric field of a capacitor is voltage over distance.
A. If you add a resistor that is connected to the capacitor in series, it will decrease the voltage applied to the capacitor as the same amount of current has to flow through each.
B. If we had a resistor that is connected to the capacitor in parallel, the voltage drop will not change across the capacitor.
C. This one is obvious knowing E=V/d.
D. How do you know the battery will increase the voltage, thus increasing the electric field of the capacitor.
Circuits MCAT mastery page 206 question 14
The big picture is that we have two resistors in parallel. The middle series of resistors add up to effectively one resistor with a resistance of 12 ohms.
We can then calculate two resistors in parallel to calculate the total resistance of the system.
Fun, if we were given voltage, we could solve for the current given total resistance. If we were given current, we could solve for voltage of the system. V=IR
MCAT mastery circuits page 208 question 15
Ammeter attempts to determine the flow of charge at a single point and should not contribute to the resistance of a circuit, therefore they should have no resistance.
Voltmeters are attempting to determine a change in potential from one point to another. To do this, they should not provide an alternative route for charge to flow and should therefore have infinite resistance.
Relevant equations and relationships for circuits chapter 6
