Question

When the key K is pressed at time t = 0, then which of the following statement about the current I in the resistor AB of the given circuit is true?

• A. I oscillates between 1 mA and 2 mA
• B. at t = 0, I = 2 mA and with time it goes to 1 mA
• C. I= 1 mA at all t
• D. I= 2 mA at all t.

Answer 1

Answer: (B)

at t = 0, I = 2 mA and with time it goes to 1 mA

Answer 2

Initially, the current will pass through the capacitor (and not through the resistance which is parallel to capacitor). So effective resistance in the circuit is $R_{AB}$. Therefore the current in the resistor is 2 mA. After some time, the capacitor will become fully charged and will be in its steady state. Now no current will pass through the capacitor and the effective resistance of the circuit will be (1000 + 1000) = 2000 $\Omega$. Therefore current in the resistor $=\frac{V}{R}=\frac{2}{2000}=1\times10^{-3} A=1 mA.$