Can You Calculate the Charges on Capacitor Plates in a Series Circuit?

[Apteronotus]

Hi I have a question regarding the charge Q that would build up on capacitors in series when there is a potential difference between the plates.

Consider the attached circuit.
1. Knowing the potentials \phi_A, \phi_B and the capacitances C_A, C_B, but not \phi_C is there a way of calculating the charges on the plates?

2. Is Q_A=Q_{Ca} and Q_B=Q_{Cb}?

3. Is Q_{Ca}=Q_{Cb}? If not, what would prevent charge flowing from one plate to the other?

4. The series capacitors are equivalent to a single capacitor having capacitance
C_T=(C_AC_B)/(C_A+C_B) and hence charge Q_T=C_TV. Is Q_A=Q_B=Q_T?

Sorry this is so long winded, and thanks in advance.

 

[berkeman]

Hi I have a question regarding the charge Q that would build up on capacitors in series when there is a potential difference between the plates.

Consider the attached circuit.
1. Knowing the potentials \phi_A, \phi_B and the capacitances C_A, C_B, but not \phi_C is there a way of calculating the charges on the plates?

2. Is Q_A=Q_{Ca} and Q_B=Q_{Cb}?

3. Is Q_{Ca}=Q_{Cb}? If not, what would prevent charge flowing from one plate to the other?

4. The series capacitors are equivalent to a single capacitor having capacitance
C_T=(C_AC_B)/(C_A+C_B) and hence charge Q_T=C_TV. Is Q_A=Q_B=Q_T?

Sorry this is so long winded, and thanks in advance.

Capacitors are DC open circuits, so the voltage in the middle is indeterminate, in a sense.

But the way this problem is usually stated, you turn on the voltage source and ramp it up to its final voltage V. During this ramping process, a current flows through the capacitors according to the traditional equation:

I(t) = C \frac{dV(t)}{dt}

That current results in charge displacement, which gives the final voltage values on the caps. You are correct that the series combination of the two caps results in a lower overall series equivalent capacitance. If the caps are unequal in capacitance value, the larger one will end up with a lower voltage across it.

Now with that, are you able to answer your questions?

 

[berkeman]

Oh, and remember that I(t) = \frac{dQ(t)}{dt}