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Helga [31]
3 years ago
10

Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1. What is the ratio (U_{\rm C})_1/\,(U_{\r

m C})_2.
Physics
1 answer:
IrinaK [193]3 years ago
4 0

Answer:

1/2

Explanation:

The energy stored in a capacitor is given by

U=\frac{1}{2}CV^2

where

C is the capacitance

V is the potential difference

Calling C_1 the capacitance of capacitor 1 and V_1 its potential difference, the energy stored in capacitor 1 is

U=\frac{1}{2}C_1 V_1^2

For capacitor 2, we have:

- The capacitance is half that of capacitor 1: C_2 = \frac{C_1}{2}

- The voltage is twice the voltage of capacitor 1: V_2 = 2 V_1

so the energy stored in capacitor 2 is

U_2 = \frac{1}{2}C_2 V_2^2 = \frac{1}{2}\frac{C_1}{2}(2V_1)^2 = C_1 V_1^2

So the ratio between the two energies is

\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}

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