JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Current Electricity

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 $t = ln 2$ 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

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 = \infty

, capacitors are fully charged and no current flows. Voltmeter reads +5V. ✓ (A)

The time constant

τ = 1

s. Current decays as

I = I_{0} e^{- t / τ}

, so at

t = 1

I = I_{0} / e

. ✓ (C)

At

t = \infty

, current becomes zero. ✓ (D)

Voltmeter reading:

V (t) = 5 (1 - e^{- t}) - 5 e^{- t} = 5 (1 - 2 e^{- t})

. At

t = ln 2

V = 0

. ✓ (B)

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · One or more correct options

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JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Current Electricity

Solution

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