Question

The switch S shown in figure (32−E35) is kept closed for a long time and is then opened at t = 0. Find the current in the middle 10 Ω resistor at t = 1 ms.
Figure

Answer 1

The current is 11 mA in the middle 10 Ω resistor at t = 1 ms.

Explanation:

• There was a closure of switch S initially. So, the capacitor was charged. Also, there is a parallel connectivity between the two resistors. The circuit’s equivalent resistance, R = 110 + 1110 = 5 Ω

• Firstly, there was a closure of switch and the charging of the capacitor. Thus, the two resistances were in parallel connection. Hence, 5 Ω will be their effective resistance.

• Across the 10 Ω resistance, the potential difference is V = 125 $\times$ 10 = 24 V.

When the switch is opened, through the capacitor, the decay of charge is,

Q = Q0 e-tRC = V $\times$ C e-tRCtRC = 1000250 = 4

⇒Q = 24 $\times$ 25 $\times$ 10-6 $\times$ e-4 = 10.9 $\times$ 10-6C

In the 10 Ω resistor, the current is I = Qt = 10.9 $\times$ 10-3 sec $\times$ 10-6 C1 = 11 mA.