Capacitor charge in series and parallel circuit

In summary, three capacitors with capacitances C1 = 4.0 μF, C2 = 3.0 μF, and C3 = 2.0 μF are connected to a 12-V voltage source. We need to find the charge on capacitor C2. To do this, we need to first find the total capacitance of C2 and C3, which are connected in parallel. Using the equation Ceq = C1 + C2, we get a total capacitance of 5.0 μF. This combined capacitance is then in series with C1, and using the equation Q = VC, we can find the charge on C2 by multiplying the voltage by the proportion of C
  • #1
Joshb60796
62
0

Homework Statement



Three capacitors, with capacitances C1 = 4.0 μF, C2 = 3.0 μF, and C3 = 2.0 μF, are
connected to a 12 -V voltage source, as shown in the figure. What is the charge on
capacitor C2 ?

Homework Equations


Q=VC
Q = charge
V = voltage
C = capacitance
Ceq = equivalent capacitance

The Attempt at a Solution



C1 and C2 are in series and therefore should be summed as in Ceq=1/((1/C1)+(1/C2)) because the voltage across them will be shared proportionally. If I multiply Ceq by the voltage I get a charge of Q12 which is for both capacitors. I need to find the charge on C2 so I am multiplying the charge on both, Q12, by the proportion of C2 to C1 which is 3/4. I am getting 15.4 microCoulombs but my answer should come to 16 microCoulombs. I need help on this questions. Am I doing this correctly? Is my thought process correct?
 

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  • #2
(try using the X2 button just above the Reply bos

Hi Joshb60796! :smile:

(try using the X2 button just above the Reply bos :wink:)
Joshb60796 said:
C1 and C2 are in series …

Nooo :redface:

C2 and C3 are in parallel, and then C1 is in series with their resultant.

Try again. :smile:
 
  • #3
tiny-tim said:
Hi Joshb60796! :smile:

(try using the X2 button just above the Reply bos :wink:)


Nooo :redface:

C2 and C3 are in parallel, and then C1 is in series with their resultant.

Try again. :smile:

I was aware that C2 and C3 were parallel which is why I didn't include C3. Aren't C2 and C3 seeing the same voltage so if the voltage is connected for a long time C3 doesn't factor into the charge that is held on C2? I thought it was just Capacitance and Voltage that has to do with Charge, Q.
 
  • #4
Joshb60796 said:
Aren't C2 and C3 seeing the same voltage …

yes :smile:
so if the voltage is connected for a long time C3 doesn't factor into the charge that is held on C2?

yes it does, C2 has to share its charge with C3 (and btw, not equally)
I thought it was just Capacitance and Voltage that has to do with Charge, Q.

yes, but you have to use the total capacitance of C2 and C3 combined to find how that combines with C1 :wink:

find the capacitance of C2 and C3,

then find the total capacitance …

show us what you get :smile:
 
  • #5


Your thought process is correct, but there may be a small error in your calculation. When finding the equivalent capacitance for capacitors in series, the formula is Ceq = 1/((1/C1)+(1/C2)). However, in your calculation for the charge on C2, you are using the formula Ceq=1/((1/C1)+(1/C2)) instead of Ceq = (C1 * C2)/(C1 + C2). Using the correct formula, the charge on C2 should be 16 microCoulombs.
 

1. What is the formula for calculating the total capacitance in a series circuit?

In a series circuit, the total capacitance (Ceq) is equal to the reciprocal of the sum of the reciprocals of each individual capacitance (C1, C2, etc.):
Ceq = 1/(1/C1 + 1/C2 + ...)

2. How does the total charge in a series circuit compare to the individual charges on each capacitor?

In a series circuit, the total charge (Qeq) on each capacitor is equal to the charge (Q) on any one capacitor. This means that the charge is the same on all capacitors in a series circuit.

3. What is the formula for calculating the total capacitance in a parallel circuit?

In a parallel circuit, the total capacitance (Ceq) is equal to the sum of the individual capacitances (C1, C2, etc.):
Ceq = C1 + C2 + ...

4. How does the total charge in a parallel circuit compare to the individual charges on each capacitor?

In a parallel circuit, the total charge (Qeq) is equal to the sum of the charges (Q) on each individual capacitor. This means that the total charge is equal to the sum of the individual charges on each capacitor in a parallel circuit.

5. What happens to the total capacitance in a series or parallel circuit when more capacitors are added?

In a series circuit, the total capacitance decreases as more capacitors are added because the individual capacitances add in a reciprocal manner. In a parallel circuit, the total capacitance increases as more capacitors are added because the individual capacitances add together.

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