In the circuit shown below, the key is pressed at time t = 0 . Which of the following statements (s) is (are) true?

Options

A. The voltmeter displays `-5v` as soon as the key is pressed, and displays +5V after a long time
B. The voltmeter will display 0 V at time t = In 2 seconds
C. The current in the ammeter becomes `1//e` of the initial value after 1 second
D. The current in the ammeter becomes zero after a long time

Answer

A, B, C, D

Explanation

Just after pressing key,`5-25000i_1=0, 5-500000 i_2=0`
(As charge in both cap=0)
`implies i_1=0.2 mA implies i_2=0.1 mA`
and `V_B+25000i_1=V_A implies V_B-V_A=-5V`
`implies 5-(q_1)/(40)=0 implies q_1=200 muC`
`5-(q_2)/(20)=0 impliesq_2=100 muC`
`V_B-q_2/(20)=V_A impliesV_B-V_A=+5V implies` (A) is correct
For capicitor `1,q_1=200[1-e^(-t//1)]muC` ,`i_1=1/5e^(-t//1)mA`
For capacitor `2,q_2=100[1-e^(t//1)]muC ,i_2=1/10e^(-t//1)mA`
`V_s-q_2/(20)+i_1xx25=V_A implies V_B-V_A=5[1-e^(-t)]-5e^(-t)=5[1-2e^(-t)]`
At`t=1n2,V_B-V_A=5[1-1]=0 implies ` (B) is correct .
At `t=1, i=i_1+1_2=1/5e^(-1)+1/10e^(-1)=3/(10).1/e`
At `t=0, i=i_1+i_2=1/5+1/10=3/10 implies` (C) is correct
After a long time,`i_1=1_2=0 implies` (D) is correct.