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← IIT-JEE 2010 · Paper 2
PhysicsInteger+3Question 46 of 57

IIT-JEE 2010 · Paper 2, Physics question 46

At time t=0t=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: ln⁡5=1.6\ln5=1.6, ln⁡3=1.1\ln3=1.1]

Between A and B: two 2 MΩ resistors in parallel, in series with two 2 μF capacitors in parallel.
Answer and worked solution

Official answer: 2

Equivalent circuit. Two 2 MΩ in parallel: 1 MΩ. Two 2 μF in parallel: 4 μF. Time constant τ=RC=4\tau=RC=4 s.

Charging. V=10(1−e−t/4)=4V=10\left(1-e^{-t/4}\right)=4 gives e−t/4=0.6e^{-t/4}=0.6:
t=4ln⁡53=4(ln⁡5−ln⁡3)=4(1.6−1.1)=2 s.t=4\ln\frac53=4(\ln5-\ln3)=4(1.6-1.1)=2\text{ s}.

Answer: 2

Topics:RC circuits
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