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(D) In circuit $(A)$, the impedance is $Z_A = R = 30 \ \Omega$. The r.m.s. current is $I_A = V/Z_A = 210/30 = 7 \ A$.In circuit $(B)$, the impedance i

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The r.m.s. current in $(B)$ can never be larger than that in $(A)$

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(D) In circuit $(A)$, the impedance is $Z_A = R = 30 \ \Omega$. The r.m.s. current is $I_A = V/Z_A = 210/30 = 7 \ A$.In circuit $(B)$, the impedance is $Z_B = \sqrt{R^2 + (X_L - X_C)^2}$.Here, $X_L = 2\pi fL = 2 	imes 3.14 	imes 50 	imes 40 	imes 10^{-3} \ \Omega \approx 12.56 \ \Omega$.$X_C = 1/(2\pi fC) = 1/(2 	imes 3.14 	imes 50 	imes 0.4 	imes 10^{-6}) \ \Omega \approx 7961.78 \ \Omega$.Since $X_C \gg X_L$, the impedance $Z_B$ is much larger than $R$, so $I_B = V/Z_B However, if the frequency $f$ is varied such that the circuit $(B)$ reaches resonance $(X_L = X_C)$, then $Z_B = R = 30 \ \Omega$. At resonance, $I_B = V/R = 7 \ A$, which is equal to $I_A$. If the circuit parameters were different or if we consider the voltage across components, the current in $(B)$ can be manipulated. Specifically, in an $LCR$ circuit, the current can be equal to the resistive circuit current at resonance. The statement that the r.m.s. current in $(B)$ can be larger than that in $(A)$ is incorrect because the maximum current in an $LCR$ series circuit is limited by the resistance $R$, which is the same as in circuit $(A)$. Thus, the current in $(B)$ can at most be equal to the current in $(A)$. Therefore, the correct option is $(D)$.

Given below are the two circuits, choose the correct option.

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