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Question

A source of emf E=10 V and having negligible internal resistance is connected to a variable resistance. The resistance varies as shown in figure. The total charge that has passed through the resistor R during the time interval from t1 to t2 is


A
40loge4
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B
30loge3
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C
20loge2
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D
10loge2
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Solution

The correct option is D 10loge2
Let R=at+b
At t=10 s,R=20 Ω

20=10a+b ...(1)

At t=30 s,R=40 Ω

40=30a+b ...(2)

Solving these two equations, we get

a=1 Ωs1 and b=10 Ω

R=(t+10)

Since, i=ER=10t+10

and Δq=3010idt

Δq=3010(10t+10)dt

Δq=10loge(2)
Hence, the correct answer is (D).

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