Refer to the circuit diagram and the corresponding graphs. The current rises when key K is pressed. With R = R₁ and L = L₁ the rise of current is shown by curve (1), while curve (2) shows the rise of current when R=R₂ and L = L₂. The maximum current is same for the both curves, then

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$R > R_{2}, L_{1} = L_{2}$

$R_{1} > R_{2}, L_{1} < L_{2}$

$R_{1} = R_{2}, L_{1} > L_{2}$

$R_{1} = R_{2}, L_{1} < L_{2}$

answer is D.

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Detailed Solution

Consider the expression for the current rising exponentially in the LR circuit. The time constant is (L/R). In this case the curve (1) is rising faster than curve (2) indicating that $(L_{1} / R_{1}) < (L_{2} / R_{2})$ . However, in both the cases the maximum current is the same and equal to $(V / R_{1})$ or $(V / R_{2})$ , which means $R_{1} = R_{2}$