An inductor of reactance 100 text{ } Omega, a | vedclass

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(A) Given: Inductive reactance $X_L = 100 	ext{ } \Omega$, Capacitive reactance $X_C = 50 	ext{ } \Omega$, Resistance $R = 50 	ext{ } \Omega$, Volt

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(A) Given: Inductive reactance $X_L = 100 	ext{ } \Omega$, Capacitive reactance $X_C = 50 	ext{ } \Omega$, Resistance $R = 50 	ext{ } \Omega$, Voltage $V = 10 	ext{ V}$.
First, calculate the impedance $Z$ of the $LCR$ series circuit:
$Z = \sqrt{R^2 + (X_L - X_C)^2}$
$Z = \sqrt{50^2 + (100 - 50)^2} = \sqrt{50^2 + 50^2} = \sqrt{2 	imes 50^2} = 50\sqrt{2} 	ext{ } \Omega$.
The current in the circuit is $I = \frac{V}{Z} = \frac{10}{50\sqrt{2}} = \frac{1}{5\sqrt{2}} 	ext{ A}$.
The average power dissipated in an $AC$ circuit is given by $P = I^2 R$.
$P = \left(\frac{1}{5\sqrt{2}}ight)^2 	imes 50 = \frac{1}{25 	imes 2} 	imes 50 = \frac{50}{50} = 1 	ext{ W}$.

An inductor of reactance $100 \text{ } \Omega$, a capacitor of reactance $50 \text{ } \Omega$, and a resistor of resistance $50 \text{ } \Omega$ are connected in series with an $AC$ source of $10 \text{ V}$, $50 \text{ Hz}$. Average power dissipated by the circuit is (in $\text{ W}$)

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