(A) For an $LCR$ series circuit,the impedance $Z$ is given by the formula: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ Given: $X_L = R$,$X_C = 2R$,and resistance

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(A) For an $LCR$ series circuit,the impedance $Z$ is given by the formula: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ Given: $X_L = R$,$X_C = 2R$,and resistance $= R$. Substituting these values into the impedance formula: $Z = \sqrt{R^2 + (R - 2R)^2}$ $Z = \sqrt{R^2 + (-R)^2} = \sqrt{R^2 + R^2} = \sqrt{2R^2} = R\sqrt{2}$ The power factor of an $LCR$ circuit is defined as $\cos \phi = \frac{R}{Z}$. Substituting the value of $Z$: $\cos \phi = \frac{R}{R\sqrt{2}} = \frac{1}{\sqrt{2}}$

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

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An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

TS EAMCET 2024 All TS EAMCET

A
$\frac{1}{\sqrt{2}}$
B
$\frac{1}{\sqrt{3}}$
C
$\frac{1}{4}$
D
$\frac{\sqrt{3}}{2}$

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An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

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