3.2 - Complete Electrical Cicuits Flashcards
What are 2 of the fundamental rules governing measurements in electrical circuits
The conservation of charge and conservation of energy - these determine how current, voltages and resistances change around any particular circuit
Tell me about the total amount of charge in a circuit
The total amount of charge within a circuit cannot increase or decrease when the circuit is functioning.
Where must current be measured
Currents are measures of charge flow through a component, so they must be measured in the same line as the component eg ammeter must always be placed in series next to component
Does an ammeter have high or low resistance
must have very low resistance to avoid significant alteration of the current it is to measure - resistance of ammeter can’t affect reading
What’s current like In series circuits
Any group of components that follow in series in a circuit, with no junctions in the circuit, must have the same current through them all
What’s current like in parallel
Whenever a current goes through a junction in a circuit, the charges can only go one way or the other, so current must split.
The proportions that travel along each possible path will be in inverse proportion to the resistance along that path - if path has high resistance, current less likely to go that way
But the total along the branches must add up to the original total current in order to conserve charge
How are voltages measured in circuits
Voltmeters must always be in parallel across the component they are measuring
Voltages are measures of energy change as charge passes through a component, so they must be measured from one side to the other so it is placed in parallel across the component
Why do voltmeters have high resistance
A voltmeter measures the voltage difference between two different points of a component but it should not change the amount of current going through the element between those two points. So, it should have very high resistance so that it doesn’t “draw” current through it.
What is voltage like in series circuits
Any group of emfs that follow in series in a circuit, with no junctions in the circuit, will have a total emf that is the sum of their individual values, accounting for the direction of their positive and negative sides
Eg two 1.5v bells in series will supply an emf of 3 V
Take account for their directions, as cells in opposite directions oppose eachother and cancel out the emf they would supply
What are voltages in parallel circuits like
If the voltage across any branch of a circuit is know then the voltage across any other branch in parallel with it will be identical
Eg a voltmeter read 6V on one branch so the voltage is the same acros all parallel branches within a circuit
How is resistance found / measured
Resistance can be calculate from ohms lass as V/I - this can be done for any individual component or a whole branch of a circuit as long as current and voltage is known
What’s resistance in series like
Any group of resistances that follow in series in a circuit, with no junctions in the circuit, will have a total resistance that is the sum of their individual values
Total R = total V / I
R total = R1 + R2 + …
Should be account for resistance of ammeter and voltmeter
Ammeters in series and voltmeters in parallel do not affect the total resistance and so can be ignored
How do we do the derivation of Rtotal = R1 + R2 + R3
Derive resistance in series
Resistors in series will have a total pd across them that is the sum of their individual pds
Current through them will be the same for each one so
Vtotal = V1 + V2 + V3
V = IR IRtotal = IR1 + IR2 + IR3
Since I is the same
It becomes Rtotal = R1 + R2 + R3
What is resistance like in parallel
the total resistance of a group of resistors in parallel can be calculated from the equation
1/Rtotal = 1/R1 + 1/R2 + 1/R3
Resistors in parallel follow a reciprocal sum rule to find their total resistance
Any combination of resistors in parallel will have a total resistance that is smaller than the smallest individual resistance in the group
How do we derive the rule of resistors in parallel
Resistors In parallel will have a total current through them that is the sum of their individual currents in branches. The pd across them will be the same for each branch
Itotal = I1 + I2 + I3
I= v / R
V/Rtotal = V/R1 + V/R2 + V/R3
Therefore
1/Rtotal = 1/R1 + 1/R2 + 1/R3
How do we find resistance when resistors are in branch combinations
If a circuit has a mixture of series and parallel combinations, we must use the rules we have for each group of resistors and then use the rules again to combine these sub-totals
Calculate total resistance of resistor groups separately, before using the appropriate rule to combine the sub totals together
How can we investigate circuit rules (practical)
Make a complex circuit with various components in series and parallel combinations
Using only ammeter and voltmeter, your partner should be able to verify the circuit rebukes explained in this sections - if the resistances are large, ammeter may need to be a multimeter set to read milliamperes currents
Join various resistors in various combinations of series and parallel connections. Your partner should be able to calculate what they expect the overall resistance of the combination to be - check wether they are right by measuring overall resistance of the resistor combination using an ohm meter
Who was Gustav Kirchoff
A physicist who presented the conservation of charge and of electrical energy within a circuit as 2 laws of physics
What’s the electric current rule
Electric current rule: the algebraic sum of the currents entering a junction is equal to zero
Weird E (symbol for the sum of) I (current) = 0 EI = 0
In order to conserve electric charge, the sum of all the currents arriving at any point (such as a junction) in a circuit is equal to the sum of all the currents leaving that point.
Tell me about the electric voltages rule
In order to conserve electrical energy around any closed loop in a circuit, the sum of the emfs is equal to the sum of the pds around that loop - loop must be complete
If current flowing the same direction as components and cell - voltages all in the same direction So Ee(e for emf) = EV
If there is no Emfs (supply voltages) then look at directions of closed loop and Ee = 0 therefore Ev = 0
Tell me about voltages rule with calculated pds
Potential differences are the product of currents passing through resistances, in order to use up electrical energy. Thus, each pd can be calculated from Ohms law as V = IR
So Ee = EIR
What’s the electric current rule
The algebraic sum of the currents entering a junction is equal to zero
EI = 0
What’s the voltages circuit rule
Around a closed loop, the algebraic sum of the emfs is equal to algebraic sum of the pds
Ee = EIR
How does voltage split up in s circuit
We have seen that all the voltage supplied by emfs in a circuit loop must be used by components as potential differences at other points around the circuit loop
The way that the voltage splits up is in propotion to the resistance of the components in the circuit loop
Tell me an example of a potential divider circuit
The voltages across 2 resistors must add up to 6V (supply), the 20 ohm resistor has twice the resistance so takes twice the voltage of the 10ohm resistor - this is a potential divider circuit
How does ohms law explain why the voltage is split in proportion to the resistance
Consider 2 resistors with residences R1 and R2, and their corresponding voltages (V1 and V2)
- calculating the current through each one gives
I1 = V1/R1 and I2 = V2/R2
But they both have the same current through them so I1 = I2 therefore
V1/R1 = V2/R2
Therefore
V1/V2 = R1/R2
What does V1/V2 = R1/R2 tell us
So the voltage is split in the same proportion as the ratio of the resistance for any Values of resistance
This means that for a known emf supply voltage, we can use Carefully chosen resistances to share the voltage and provide a specific value of pd on one component
If we then also remember that all parallel branches in a circuit must have the same voltage, then any branch we set up in parallel with that specific pd will also have the same voltage, thus we can set up a circuit to provide an exaclty chosen value of voltage to the parallel branch
Using variable resistors, this set up can then be used to prove whatever voltage we choose - particularly useful if emf is a fixed value like a battery
What happens when we adjust a variable resistor
Adjusting the variable resistor alters the proportion of the voltage it takes, and so the pd that is left for the resistance wire /(any other component - resistance wire just an example)can be varied to any value we choose
If variable resistor set to high resistance, it will have high pd and so only a little bit for the redtisnce wire (or any other components that are there)
How do we use a potential divider circuit to make an IV graph
By changing the resistance of the variable resistor, the pd across the component being measured will change - we can adjust variable resistor to a set of value of pd on the component to those we need of I-V graph plot
Tell me about the potential divider equation
As the pd in a potential divider circuit is split in proportion to the resistances of the components, we can calculate the pd across them mathematically
Vout is the thing we want to calcaulte and v In is the supply voltage
R2 is usually the restisnce of the component we want
Vout = Vin x (R2/R1 + R2)
