Physics - Capacitor Question with Solution | TestHub

Initial energy stored: $U_0=\frac{1}{2}C{V}^2=\frac{1}{2}\times 3\mu F\times (100{)}^2=1.5\times 10^{-2}J$

Time constant: $\tau =RC=3\times 3=9\mu s$

Charge remaining at time t: q = q₀e^(−t/τ); energy left ∝ q², so heat developed till t:$H=U_0\left(1-e^{-2t/\tau }\right)$

At t = 9 μs = τ:$H=1.5\times 10^{-2}\left(1-e^{-2}\right)=1.5\times 10^{-2}\left(\frac{e^2-1}{e^2}\right)=3\left(\frac{e^2-1}{2e^2}\right)\times 10^{-2}J$

Comparing with $\eta \left(\frac{e^2-1}{2e^2}\right)\times 10^{-2}J$: η = 3. Answer: 3