JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Current Electricity

At time

t = 0

, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?
[Take :

ℓ n 5 = 1.6, ℓ n 3 = 1.1

]

Answer: 2

Solution

The voltage across a charging capacitor is:

V_{C} = V_{0} (1 - e^{- t / R C})

From the circuit, the equivalent time constant is

τ = R C = 4

s.

When

V_{C} = 4

4 = 10 (1 - e^{- t /4})

0.4 = 1 - e^{- t /4}

e^{- t /4} = 0.6

- \frac{t}{4} = ln (0.6) = ln (3/5) = ln 3 - ln 5 = 1.1 - 1.6 = - 0.5

t = 2 seconds

The answer is 2.

JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Integer answer

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