Question

The switch S is kept closed for a long time in fig 20.50. It is opened at t=0. Find the current in $R_1$ at t=1ms.

• A. 11.2 mA
• B. 12.4 mA
• C. 13.4 mA
• D. 14.4 mA

Answer 1

The correct option is C 13.4 mA

Just after reopening the switch, the capacitor will start discharge through $R_1$ and that time ammeter reading . When switch S is open , the capacitor will start discharging. The equation of discharging is

$Q\left(t\right)=Q_0{e}^{-t/CR}$

The current in $R_1$ is $I=\frac{dQ}{dt}=Q_0(-1/CR)e^{-t/CR}$

in magnitude, $I=\frac{CV}{RC}{e}^{-t/CR}=\frac{V}{R}{e}^{-t/CR}=\frac{20}{10}{e}^{-\frac{{10}^{-3}}{20\times {10}^{-6}\times 10}}=2e^{-5}=13.4mA$