Circuits

Question 1

What is current?

Answer 1

Current is the flow of positive charge.

• Current flows in the direction from the positive terminal to the negative terminal.
• This is counter-intuitive because electrons flow in the opposite direction.

Question 2

In a wire, a 2 C charge flows through it. How much time must it take for that 2 C charge to flow in order to produce a 8 A current?

Answer 2

0. 25 seconds
   * (2 C) / (0.25 A) = 8 A

Question 3

What are the two primary types of conductivity tested on the MCAT?

Answer 3

Metallic conductivity and electrolytic conductivity.

• The more solutes dissolved in solution the better the conductivity for electrolytic conductivity.
  
  • If there isn’t enough solute dissolved, then the current may be very weak.

Question 4

What is Kirchhoff’s Junction Rule?

Answer 4

Kirchhoff’s Junction Rule states that the sum of currents entering into any point or junction must equal the amount of current leaving that point.

• In layman’s terms: Current entering the circuit must equal current exiting the circuit
• Kirchhoff’s Laws state energy and charge are conserved in a circuit.

Question 5

What is resistivity and how is it calculated?

Answer 5

Resistivity is the opposition to the flow of current/charge. The formula for calculating resistance (which is measured in Ohms) is:

Question 6

How does temperature affect resistance of must conductors?

Answer 6

As temperature increases, resistance increases in most conductors.

Question 7

What is Ohm’s Law?

Answer 7

Ohm’s Law is used to calculate the resistance any resistor in a circuit. The formula for Ohm’s Law is:

V = I x R or I = V/R

I = Current (A)

V = Voltage or Voltage Drop (V)

R = Resistance (Ohms)

Question 8

What is electromotive force (EMF)?

Answer 8

Electromotive force is the force that a battery or any other power source has the capability to deliver to a circuit.

• When charge is not actually moving (not connected to a circuit), the difference is referred to as the electromotive force (EMF) measured in Volts.

Question 9

How do you calculate the actual voltage supplied by a battery (cell)?

Answer 9

All batteries (cells) have their own measurable amount of internal resistance. If there is no current flowing, then there is no internal resistance (V = E_cell).

• Formula for calculating the actual voltage supplied by a cell: V = E_cell - (I x R_int)
  
  • V = Voltage provided by cell (V)
  • E_cell = electromotive force (emf) of cell (V)
  • I = Current (A)
  • R_int = Internal resistance of cell (Ohms)
• If the battery is not connected to a circuit ( no current flowing), then the voltage supplied by the battery/cell is equal to the electromotive force.

Question 10

What are the units that compose an ampere (unit for current)?

Answer 10

Amperes are measured or composed of coulumbs/sec.

Question 11

What is the difference between direct and alternating current?

Answer 11

Direct current flows in only one direction in a circuit. Alternating current can change the direction of current flow periodically in a circuit.

• Very rare for alternating current to be tested on the MCAT although it is not out of scope.

Question 12

What causes current to flow?

Answer 12

The potential difference (voltage) in a battery or generator causes charge to move.

Question 13

What are watts and what do the measure?

Answer 13

Watts (W) are electricity’s version of power and is measured in Joules/second. Watts measure the rate at which energy is transgerred or transformed.

• In image below, power (P) is interchangeable with watts (W).

Question 14

What are all the important equations related to Resistors that are tested on the MCAT?

Answer 14

P=Power=Watts(W) (J/s)

Question 15

What are capacitors and what do they do?

Answer 15

Capacitors store charge based on voltage (J/C) and then rapidly release/discharge it.

• C = (Q/V)
  
  • Helps measure capacitance (C) in a circuit
• C = Σ₀ x (A/d)
  
  • Used to calculate physical properties of capacitors

Question 16

A capacitor has a capacitance of 8 F. Its area is doubled and the distance between its plates is quadrupled. What is the new capacitance?

A. 1 F

B. 4 F

C. 8 F

D. 16 F

Answer 16

Answer: 4 F

The two changes can be approached one at a time, keeping in mind the proportions of the capacitance equation: C is directly proportional to A, but inversely proportional to d. A is doubled, so C is doubled to 16 F. The distance is then multiplied by 4, so the capacitance is divided by 4, to 4 F.

Question 17

In what direction do electric fields travel/point and what are the equations that relate electric fields to parallel plate capacitors?

Answer 17

Electric fields point in the positive to negative direction.

Question 18

What is the equation that relates potential energy (U) to capacitance (C)?

Answer 18

Question 19

A charged capacitor holds 4 J of potential energy. Its capacitance is cut in half while its voltage is doubled. How much energy does the capacitor now hold?

A. 2 J

B. 8 J

C. 12 J

D. 16 J

Answer 19

Answer: 8 J

The potential energy (U) stored in a capacitor is directly proportional to its conductance (C) and directly proportional to the square of its voltage (V). C is divided by 2, so the energy stored goes from 4 J to 2 J. V is doubled, so energy increases by a factor of 4, from 2 J to 8 J.

Question 20

What are dielectrics?

Answer 20

Dielectrics are insulating material that increase capacitance by preventing stray charges from crossing the gap or distance between capacitor plates.

• The equation C’ = k x C helps calculate the new, increased capacitance based on the dielectric inserted.
  
  • k is the dielectric constant unique to a specific material/substance

Question 21

How does capacitance increase when a dielectric is inserted into a capacitor in a circuit vs an isolated capacitor (no circuit)?

Answer 21

In closed circuit, a dielectric will increase the charge (Q) that builds on the capacitor, while the voltage (V) will remain constant.

An isoloated capacitor that has a dialectric inserted will not affect charge (Q) as charge is not flowing, but will decrease voltage (V).

• C = (Q / V)

Question 22

Dielectrics _______ capacitance in circuit capacitors and _______ capacitance in isolated capacitors.

Answer 22

Increase, Increase

• Dielectrics always increase capacitance
• The capacitance of both circuit and isolated capacitors are increased by the insertion of a dielectric material. In isolated capacitors, the increase in capacitance arises from a decrease in voltage. In circuit capacitors, instead the stored charge increases and voltage remains the same.

Question 23

Two capacitors are connected in series. One has a capacitance of 10 F, and the other has a capacitance of 30 F. What is total capacitance of that stretch of circuit?

Answer 23

Answer: 7.5 F

Capacitors in series are added using reciprocals: 1/C = 1/10 + 1/30. So, 1/C = 3/30 + 1/30, so 1/C = 4/30. We can then flip both sides of the equation. C = 30/4 = 7.5 F.

Question 24

What are the key equations associated with capacitance?

Answer 24