AP Physics C Electricity : Using Capacitor Equations

Example Questions

Example Question #1 : Capacitors

You are hired to make a capacitor out of two parallel metal sheets. If someone wanted you to make a thin capacitor of  out of those metal sheets, and the sheets needed to be  apart, what area do the two metal plates need to be?

Explanation:

For parallel plate capacitors, the equation is .

Solve for .

Now we can plug in our given values.

Example Question #2 : Capacitors

The plates of a parallel plate capacitor are  apart and  in area. A potential difference of is applied across the capacitor. Find the capacitance.

Explanation:

Capacitance is related to plate area and distance by the equation .

Given the area and distance, we can solve for capacitance. The voltage, in this case, is irrelevant.

Example Question #212 : Ap Physics C

The plates of a parallel plate capacitor are  apart and  in area. A potential difference of  is applied across the capacitor. Compute the charge on each plate.

Explanation:

Charge on a capacitor is given by the equation . We know that the voltage is , but we need to determine the capacitance based off of the area and distance between the plates.

We can plug this value into the equation for charge.

Example Question #3 : Capacitors

The plates of a parallel plate capacitor are  apart. A potential difference of  is applied across the capacitor. Compute the magnitude of the generated electric field.

Explanation:

The electric field given by a capacitor is given by the formula . We do not have these variables, so we will have to adjust the equation.

The capacitance can be determined by the area of the plates and the distance between them.

This equation simplifies to , allowing us to solve using the values given in the question.

Example Question #4 : Capacitors

If two identical parallel plate capacitors of capacitance  are connected in series, which is true of the equivalent capacitance, ?

Explanation:

Relevant equations:

Use the series equation, replacing C1 and C2 with the given constant C:

This agrees with the general rule that the equivalent capacitance in series is less than the capacitance of any of the individual capacitors.

Example Question #8 : Capacitors

Two parallel conducting plates each have an area of  and are separated by a distance, . One plate has a charge  evenly distributed across it, and the other has a charge of . A proton (charge ) is initially held near the positive plate, then released such that it accelerates towards the negative plate. How much kinetic energy has the proton gained in this process?

Explanation:

Relevant equations:

According to the work-energy theorem, work done on the proton is equal to its change in kinetic energy.

1. Find an expression for potential difference, , in terms of  and , by setting the two capacitance equations equal to each other:

2. Multiply the potential difference times the proton charge to find work (and thus kinetic energy):

Example Question #5 : Capacitors

and  capacitor are connected in series with a  battery. What is the magnitude of the charge on one plate of the  capacitor?

Explanation:

Relevant equations:

First, find the equivalent capacitance of the whole circuit:

Use this equivalent capacitance to find the total charge:

Capacitors in series always have the same charge on each unit, so the charge on the  capacitor is also .