In an R-C circuit, we can find heat dissipated (Q) by using the equation W b = Δ U + Q Where, W b = work done by all the sources when charges flow through them and, Δ U = change in electrostatic p

Question

In an R-C circuit, we can find heat dissipated (Q) by using the equation $W_{b} = Δ U + Q$ Where, $W_{b} =$ work done by all the sources when charges flow through them and, $Δ U =$ change in electrostatic potential energy of the system of capacitors. In the given circuit at time $t = 0$ , let us close the key K . Assume $q_{0} = 2 μ C$ , $C_{1} = 1 0^{- 6} F, C_{2} = 0.5 \times 1 0^{- 6} F, R = 2Ω$ and $ε = 4 V$ ,

TestHub · Accepted Answer

Let final charge on C 2 ​ is q then by Kirchhoff's loop law at steady state, ​ C 1 ​ ( q 0 ​ − q ) ​ + C 2 ​ q ​ − ε = 0 − 2 + q × 1 0 6 + 2 × 1 0 6 q − 4 = 0 q = 2 × 1 0 6 C ​ ​ 8 × 1 0 6 = 2 × 1 0 6 + Q Q = 6 × 1 0 6 J = 6 μ J

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