How to Derive Voltage Across Capacitors in Series?

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In summary, the conversation discusses the derivation of an equation relating the voltages V_1 and V_2 in terms of V_0, C_1, and C_2 for a known voltage source connected to two capacitors in series. The equation is derived using the formula for charge on a capacitor and the total capacitance for two capacitors connected in series.
  • #1
superdave
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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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  • #2
What is the equation that relates charge Q on a capacitor to the capacitance C and the voltage V?
 
  • #3
It's V=Q/C.
 
  • #4
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?
 
  • #5
Q = CV.

In series,

1/Ctotal = 1/C1 + 1/C2 + 1/C3 Etc.
 
  • #6
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:
  • #7
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)
 

FAQ: How to Derive Voltage Across Capacitors in Series?

What is capacitance?

Capacitance is a measure of a capacitor's ability to store electric charge. It is defined as the ratio of the electric charge stored on the capacitor to the potential difference (voltage) between its plates.

What is a capacitor?

A capacitor is an electronic component that is used to store and release electrical energy. It is made up of two conductive plates separated by an insulating material. When a voltage is applied, one plate becomes positively charged while the other becomes negatively charged, creating an electric field between them.

What is the equation for calculating capacitance?

The equation for calculating capacitance is C = Q/V, where C is the capacitance in farads, Q is the charge stored on the capacitor in coulombs, and V is the potential difference (voltage) between the plates in volts.

How does the surface area of a capacitor affect its capacitance?

The capacitance of a capacitor is directly proportional to its surface area. This means that as the surface area increases, the capacitance also increases. This is because a larger surface area allows for more charge to be stored on the plates.

What factors affect the capacitance of a capacitor?

The capacitance of a capacitor is affected by several factors, including the distance between the plates, the surface area of the plates, the type of dielectric material between the plates, and the material and thickness of the plates. These factors all play a role in determining the amount of charge that can be stored on the capacitor.

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