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Initially, switch S is connected to posi...

Initially, switch S is connected to position 1 for a long time . The net amount of heat generated in the circuit after it is shifted to position 2 is .

A

`C/2 (epsilon_1 + epsilon_2)epsilon_2`

B

`C(epsilon_1+epsilon_2)epsilon_2`

C

`C/2 (epsilon_1 + epsilon_2)^2`

D

`C(epsilon_1 + epsilon_2)^2`

Text Solution

Verified by Experts

The correct Answer is:
C
c. `U_i = 1/2 C epsilon_(1)^2`
`U_f = 1/2 C epsilon_(2)^(2) , Delta U = 1/2 C (epsilon_(2)^(2) - epsilon_(1)^(2))`
`Q_("in") = + Cepsilon_1, Q_f = -Cepsilon_2, DeltaQ = abs(Q_f-Q_i) = C (epsilon_2+epsilon_1)`
Work done by battery `W_b = epsilon_2 DeltaQ = C (epsilon_2+epsilon_1)epsilon_2`
Heat generated `= W_b - DeltaU`
`= C epsilon_(2)^(2) + Cepsilon_1epsilon_2 - 1/2 C (epsilon(2)^(2) - epsilon_(1)^(2))`
`= 1/2 C (epsilon_(2)^(2) + epsilon_(1)^(2) + 2epsilon_1epsilon_2) = 1/2 C(epsilon_1 + epsilon_2)^2` .
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