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Q.

A battery of variable EMF of negligible resistance is connected to a wire with resistance of $3 Ω$ . Figure shows the potential difference across battery as function of time. The total charge transferred by the battery during two hours is :

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a

2000 C

b

1500 C

c

1800 C

d

2400 C

answer is B.

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Detailed Solution

$\begin{array}{l} V = 1.5 - (\frac{1.5}{2 \times 3600}) t \\ i = \frac{V}{R} = \frac{1.5}{3} - \frac{1}{3} (\frac{1.5}{2 \times 3600}) t ∵ i = \frac{dq}{dt} \Rightarrow dq = i dt \Rightarrow \int dq = \int i dt \\ q = \int idt = \int_{0}^{2 \times 3600} [\frac{1.5}{3} - \frac{1}{3} (\frac{1.5}{2 \times 3600}) t] dt \\ = 1800 C \end{array}$

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