Calculating Charge with Capacitors in Series

In summary, the charge on the right plate of C2 long after the switch is closed is 2V/3C. This is because Q = 1/3C * 2V is equivalent to 2V/3C, where Ceq = 1/C + 1/2C = 3/2C. However, it is important to note that the overall reciprocal must be taken into account when finding the equivalent capacitance of two capacitors in series.
  • #1
PeachBanana
191
0

Homework Statement



What is the charge on the right
plate of C2 long after the switch is
closed?

1. CV
2. CV/2
3. CV/3
4. 2CV/3
5. 0

Homework Equations



Q = CeqV

The Attempt at a Solution



Q = 1/3c * 2V
so I thought
Q = 2V/3C
 

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  • #2
PeachBanana said:

Homework Statement



What is the charge on the right
plate of C2 long after the switch is
closed?

1. CV
2. CV/2
3. CV/3
4. 2CV/3
5. 0

Homework Equations



Q = CeqV

The Attempt at a Solution



Q = 1/3c * 2V
so I thought
Q = 2V/3C
Is that (2V)/(3C) or (2V/3)C ?
 
  • #3
I wanted (2V/3)C but written that way it looks like

2CV/3 which is one of the answers but I'm trying to understand why "C" is in the numerator. Is it because Ceq = 1 / C?
 
  • #4
PeachBanana said:
I wanted (2V/3)C but written that way it looks like

2CV/3 which is one of the answers but I'm trying to understand why "C" is in the numerator. Is it because Ceq = 1 / C?

What's the net (equivalent) capacitance of the two given capacitors?
 
  • #5
Ceq = 1/C + 1/2C = 3/2C
 
  • #6
PeachBanana said:
Ceq = 1/C + 1/2C = 3/2C

Not quite. Two capacitors Ca and Cb in series yield:

$$C_{eq} = \frac{1}{\frac{1}{Ca} + \frac{1}{Cb}}$$

You've forgotten to take the overall reciprocal.
 
  • #7
I see what I did incorrectly now. My final answer should have been 2C/3.
 

FAQ: Calculating Charge with Capacitors in Series

What is the formula for calculating charge with capacitors in series?

The formula for calculating charge with capacitors in series is Q = CV, where Q is the charge, C is the capacitance, and V is the voltage.

How do you calculate the equivalent capacitance for capacitors in series?

The equivalent capacitance for capacitors in series can be calculated by adding the reciprocals of each individual capacitance and then taking the reciprocal of the sum. In other words, 1/Ceq = 1/C1 + 1/C2 + ... + 1/Cn, where Ceq is the equivalent capacitance and C1, C2, etc. are the individual capacitances.

Can you calculate charge with capacitors in series if the capacitors have different capacitance values?

Yes, you can still calculate charge with capacitors in series even if the capacitors have different capacitance values. You will need to use the formula Q = CV, where C is the equivalent capacitance of the series circuit.

What happens to the charge when capacitors are connected in series?

When capacitors are connected in series, the charge is divided between the capacitors. This means that the total charge will be less than the charge of any individual capacitor.

Can the charge on a capacitor in a series circuit be negative?

No, the charge on a capacitor in a series circuit cannot be negative. Capacitors store charge, so the charge on a capacitor will always be positive. If the calculated charge is negative, it means that the direction of the charge flow is opposite to the assumed direction.

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