AP Physics 2 : Capacitor Energy
Study concepts, example questions & explanations for AP Physics 2
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Example Questions
Example Question #1 : Capacitor Energy
Consider the circuit:
If the voltage drop across C2 is 5V, what is the total energy stored in C2 and C3?
In parallel branches of a circuit, the voltage drops are all the same. Therefore, we know that the voltage drop across C3 is also 5V.
We can then use the following equation to calculate the total stored energy:
Since the voltage is the same for both capacitors, we can simply add the two capacitances to do one calculation for energy:
Example Question #11 : Circuit Components
A 
None of the other answers is correct
To find the amount of energy stored in a capactior, we use the equation
We're given the capacitance (
Example Question #3 : Capacitor Energy
You have 4 capacitors, 
Their capacitances are as follows:
If you have a 6V battery connected to the circuit, what's the total energy stored in the capacitors?
The equation for energy stored in a capacitor is
We can find the capacitance by adding the capacitors together, and we have the voltage, so we'll use the second equation, 
When adding capacitors, remember how to add in series and parallel.
Capacitors 
Now that we have the total capacitance, we can use the earlier equation to find the energy.
The total energy stored is 121.5J.
Example Question #3 : Capacitor Energy
If 
In this circuit, the voltage source, 
To find the energy, we can use the formula
To use the formula we need the voltage across 
Another hint we can use is that 
Now, we can use the formula
Now that we know a charge of 
Finally, we plug this 
Example Question #2 : Capacitor Energy
Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is not connected to a battery. If some external agent pulls the capacitor apart such that D doubles, did the internal energy, U, stored in the capacitor increase, decrease or stay the same?
We must know the dielectric constant
Increases
Decrease
Stays constant
Increases
Equations required:
We see from the first equation the when D is doubled, C will be halved (since 
Example Question #3 : Capacitor Energy
Imagine a capacitor with a magnitude of charge Q on either plate. This capacitor has area A, separation distance D, and is connected to a battery of voltage V. If some external agent pulls the capacitor apart such that D doubles, did the internal energy, U, stored in the capacitor increase, decrease or stay the same?
Stays constant
Increases
Increases by a factor of exactly 2
Decreases
Decreases
Relevant equations:
We must note for this problem that the voltage, V, is kept constant by the battery. Looking at the second equation, if C changes (by changing D) then Q must change when V is held constant. This means that our formula for U must be altered. How can we make claims about U if Q and C are both changing? We need a constant variable in the equation for U so that we can make a direct relationship between D and U. If we plug in the second equation into the third we arrive at:
Now, we know that V is held constant by the battery, so when C decreases (because D doubled) we see that U actually decreases here. So it matters whether or not the capacitor is hooked up to a battery.
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