How to Derive Voltage Across Capacitors in Series?

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Homework Help Overview

The discussion revolves around deriving an equation for the voltage across capacitors in series, specifically relating the voltages across two capacitors, V_1 and V_2, to a known voltage source V_0 and their respective capacitances C_1 and C_2.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between charge, capacitance, and voltage, with one participant asking for the equation that relates these variables. There is also exploration of the total capacitance for capacitors in series and implications for charge and voltage across each capacitor.

Discussion Status

Some participants have provided insights into the equations governing capacitors in series, including the total voltage across the capacitors and the relationship between charge and capacitance. However, there is no explicit consensus on the final derivation or equation.

Contextual Notes

Participants are working within the constraints of deriving relationships based on given variables without providing complete solutions. The discussion includes references to fundamental capacitor equations and series connections.

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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

 
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What is the equation that relates charge Q on a capacitor to the capacitance C and the voltage V?
 
It's V=Q/C.
 
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?
 
Q = CV.

In series,

1/Ctotal = 1/C1 + 1/C2 + 1/C3 Etc.
 
Answer for you

:redface: 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)
 
Last edited:
Answer for you Superdave

:redface: 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)
 

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