A graph between current and time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circuits $R_{2}, C_{1}, C_{2}$ and $V_{1}, V_{2}$ are the values of resistance, capacitance and EMF of the cell in the two circuits. If only two parameters (out of resistance, capacitance, EMF) are different in the two circuits. What may be the correct option(s):

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$V_{1} < V_{2}, R_{1} < R_{2}, C_{1} = C_{2}$

$V_{1} = V_{2}, R_{1} > R_{2}, C_{1} > C_{2}$

$V_{1} < V_{2}, R_{1} = R_{2}, C_{1} < C_{2}$

$V_{1} > V_{2}, R_{1} > R_{2}, C_{1} = C_{2}$

answer is C.

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Detailed Solution

$\begin{array}{l} \log I = - (\frac{1}{CR}) t + \log I_{0}, I_{0} = \frac{V}{R} \\ On comparing with y = - mx + c \end{array}$

We can conclude $\frac{V_{1}}{R_{1}} = \frac{V_{2}}{R_{2}}; R_{1} C_{1} < R_{2} C_{2}$

So $V_{1} < V_{2}, R_{1} < R_{2}, C_{1} = C_{2}$

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