In the circuit shown below, the key is pressed at time t=0. Which of the following statement(s) is(are) true?
(A)The voltmeter displays -5 V as soon as the key is pressed, and displays +5 V after a long time✓ Correct
(B)The voltmeter will display 0 V at time t=ln2 seconds✓ Correct
(C)The current in the ammeter becomes 1/e of the initial value after 1 second✓ Correct
(D)The current in the ammeter becomes zero after a long time✓ Correct
Answer: (A), (B), (C), (D)
Solution
At t=0, capacitors are uncharged, so voltage across each is zero. The voltmeter reads the voltage across the 50kΩ resistor minus the voltage across the 40μF capacitor, which is -5V initially. ✓ (A)
At t=∞, capacitors are fully charged and no current flows. Voltmeter reads +5V. ✓ (A)
The time constant τ=1 s. Current decays as I=I0e−t/τ, so at t=1 s, I=I0/e. ✓ (C)
At t=∞, current becomes zero. ✓ (D)
Voltmeter reading: V(t)=5(1−e−t)−5e−t=5(1−2e−t). At t=ln2, V=0. ✓ (B)
JEE Advanced · 2016 · 22 May 2016 · Paper 2 · One or more correct options