The capacitors shown in the figure are initially uncharged. In a certain time, the capacitor of capacitance 2µF gets a charge 20µC. In that time interval, the heat produced in the 3Ω resistor is $n \times 30 m i c r o J o u l e$ . What is the value of $n$ ?

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answer is 5.

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Detailed Solution

Total charge supplied by the battery = 30µC
$\begin{array}{l} W_{B} = 30 \times 20 μJ = 600 μJ \\ U = \frac{1}{2} \times 3 \times 10^{2} = 150 μJ \\ Heat = 450 μJ \\ H_{2 Ω} = 225 μJ \\ H_{(3 Ω + 6 Ω)} = 225 μJ \\ \frac{H_{3 Ω}}{H_{6 Ω}} = \frac{6}{3} = 2 \\ \Rightarrow H_{3 Ω} = \frac{2}{3} \times 225 \\ \Rightarrow H_{3 Ω} = 150 μJ = 30 \times 5 μJ \\ \Rightarrow n = 5 \end{array}$