In the circuit shown below , key is pressed at time `t=0`, choose the correct statement.

Options

A. At time t=0, current flow through the battery is 4mA
B. At time `t to oo`, current flow through the battery is 4mA
C. At time `t to oo`, charge on capacitor is `1.2muC`
D. At time `t to oo`, charge on capacitor is `6muC`

Answer

A

Explanation

At steady state capacitor acts as open circuit
At t=0, capacitor is shorted , hence
`i=(4)/(500+500) = 4mA`
As time `t to oo`, capacitor is fully charge and offer infinite resistance
hence `i=(4)/(1000+500+500)=2mA`
Voltage across capacitor at steady state
`V_c = 1000/2000xx4 = 2V`
Charge on capacitor = Q = CV
`Q6muFxx2V = 12muC`