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RLC Circuit

Refer to the ...

Question

Refer to the circuit diagram and the corresponding graphs. The current rises when key $K$ is pressed. With $R = R_{1}$ and $L = L_{1}$ the rise of current is shown by curve (1), while curve (2) shows the rise of current when $R = R_{2}$ and $L = L_{2}$ . The maximum current is same for both curves, then :

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is D $R_{1} = R_{2}, L_{1} < L_{2}$
Consider the expression for the current rising exponentially in the $L R$ 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 $R_{1} = R_{2}$ .

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