When the rms voltages V_L, V_C and V_R are me | vedclass

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(C) In a series $LCR$ circuit,the total $rms$ voltage $V$ is given by the relation: $V = \sqrt{V_R^2 + (V_L - V_C)^2}$.Given the ratio $V_L : V_C : V_

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$90$

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(C) In a series $LCR$ circuit,the total $rms$ voltage $V$ is given by the relation: $V = \sqrt{V_R^2 + (V_L - V_C)^2}$.Given the ratio $V_L : V_C : V_R = 1 : 2 : 3$,we can express these voltages in terms of a constant $x$ as $V_L = x$,$V_C = 2x$,and $V_R = 3x$.Substituting these values into the formula for $V$:$100 = \sqrt{(3x)^2 + (x - 2x)^2}$$100 = \sqrt{9x^2 + (-x)^2}$$100 = \sqrt{9x^2 + x^2}$$100 = \sqrt{10x^2}$$100 = x\sqrt{10}$$x = \frac{100}{\sqrt{10}} = 10\sqrt{10} \approx 10 	imes 3.162 = 31.62 \, V$.Now,calculate $V_R$:$V_R = 3x = 3 	imes 31.62 = 94.86 \, V$.Rounding to the nearest given option,$V_R$ is close to $90 \, V$.

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