Example questions dealing with capacitors

Q: What would happen to the capacitance value, C, for a capacitor if the charge, q, were doubled?

A: The MCAT loves proportions, but this is a trick question. Possible answer choices could be:

a. double
b. triple
c. no change
d. cannot be determined

Without a good understanding of capacitance, many might choose a, but that is the incorrect answer. Although q and C are directly proportional, capacitance is dependent on the geometry of the capacitor. Thus, the correct answer would be c.

Q: Suppose you have two capacitors C1 = 1F and C2 = 2F. C1 is charged to a voltage of 5 V by a battery. The battery is disconnected from C1 and C1 is then connected directly to C2. What will be the potential across each capacitor?

A: This question is a bit more involved. When C1 is connected to C2, C1 will begin to discharge. The total charge on C1 will begin to disperse between the two capacitors. After all, where else can the charge on C1 go? At equilibrium, the potential differences across each capacitor will be the same. Knowing this you can solve the problem.

qtot = q1 + q2

C1Vinitial = C1V + C2V

V = VinitialC1/C1 + C2

V = 5/3 volts or about 1.67 volts

It is important to note that charge cannot be destroyed—thus the initial charge should equal the final charge.

Q: Suppose you have a capacitor connected to a battery and introduce a dielectric during charging. What happens to the potential difference and capacitance?

A: The capacitance always increases if a dielectric is introduced regardless of whether the battery is still connected. But what happens to the potential difference? It stays the same. How can it increase or decrease if it is still connected to the battery? It will be at the same potential as the battery.