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  4. Three capacitors each of capacitance C=2 μ F are connected with a battery of emf 30 V as shown in the figure. When the switch S is closed, the heat generated in the circuit will be <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-rpnieflnxvmh.png />

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Q. Three capacitors each of capacitance $C=2 \, \mu F$ are connected with a battery of emf $30 \, V$ as shown in the figure. When the switch $S$ is closed, the heat generated in the circuit will be

Question

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

$U_{i}=\frac{1}{2}C\left(\frac{V}{3}\right)^{2}+\frac{1}{2}C\left(\frac{V}{3}\right)^{2}+\frac{1}{2}\left(C\right)\left(\frac{2 V}{3}\right)^{2}$
$U_{f}=\frac{1}{2}CV^{2}$
$W_{b}=\frac{C V^{2}}{3}$
$\Delta H=\left[W_{b} - \left(U_{f} - U_{i}\right)\right]=\frac{C V^{2}}{6}=0.30mJ$