How to Derive Voltage Across Capacitors in Series?

[superdave]

Homework Statement

A known voltage source V_0 is connected by a switch to two capacitors in series with capacitance C_1 and C_2. When we flip the switch, connecting the capacitors to the voltage source, we measure the voltage across each capacitor, V_1 and V_2 respectively.

I need to derive an equation relating V_1 and V_2 in terms of V_0, C_1 and C_2

Homework Equations

The Attempt at a Solution

 

[berkeman]

What is the equation that relates charge Q on a capacitor to the capacitance C and the voltage V?

 

[superdave]

It's V=Q/C.

 

[berkeman]

Correct. Now do you know what the total capacitance is for two caps connected in series? If you know that, what can you say about the overall Q, since you know the V?

 

[Tim09]

Q = CV.

In series,

1/Ctotal = 1/C1 + 1/C2 + 1/C3 Etc.

 

[madhusudan]

Answer for you

In Series connection the the total potential difference is the sum of potential difference across each capacitor..so
V_0=V_1 + V_2
q=CV
q/c_0=q/c_1 + q/c_2
so
c_0 = (c_1*c_2)/(c_1+c_2)

 

[madhusudan]

Answer for you Superdave

In Series connection the the total potential difference is the sum of potential difference across each capacitor..so
V_0=V_1 + V_2
q=CV
q/c_0=q_1 + q_2
so
c_0 = (c_1*c_2)/(c_1+c_2)