(B) The power factor is given by $\cos \phi = \frac{R}{Z} = 0.5$.Since $R = 100 \text{ } \Omega$, we have $Z = \frac{R}{0.5} = \frac{100}{0.5} = 200 \

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(B) The power factor is given by $\cos \phi = \frac{R}{Z} = 0.5$.Since $R = 100 \text{ } \Omega$, we have $Z = \frac{R}{0.5} = \frac{100}{0.5} = 200 \text{ } \Omega$.The impedance of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Squaring both sides, $Z^2 = R^2 + (X_L - X_C)^2$.Substituting the values, $200^2 = 100^2 + (X_L - X_C)^2$.$40000 = 10000 + (X_L - X_C)^2$.$(X_L - X_C)^2 = 30000$.$|X_L - X_C| = \sqrt{30000} = 100\sqrt{3} \text{ } \Omega$.Given that the difference is $\sqrt{3}\alpha \text{ } \Omega$, we equate $\sqrt{3}\alpha = 100\sqrt{3}$.Therefore, $\alpha = 100$.

Class 12 Physics Alternating Current Inductance, Capacitance and Resistance in Series and Parallel

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An inductor of $10 \text{ mH}$, capacitor of $0.1 \text{ } \mu\text{F}$ and a resistor of $100 \text{ } \Omega$ are connected in series across an $a.c.$ power supply of $220 \text{ V}$, $70 \text{ Hz}$. The power factor of the given circuit is $0.5$. The difference between the inductive reactance and capacitive reactance is $\sqrt{3}\alpha \text{ } \Omega$. The value of $\alpha$ is . . . . . . .

JEE MAIN 2026 All JEE MAIN

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$50$
B
$100$
C
$150$
D
$200$

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Alternating Current

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Inductance, Capacitance and Resistance in Series and Parallel

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With an increase in the frequency of an $a.c.$ supply,the impedance of an $LCR$ series circuit:

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In the given circuit,the $AC$ source has $\omega = 100 \ rad/s$. Considering the inductor and capacitor to be ideal,the correct choice$(s)$ is(are):
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$(C)$ The voltage across $100 \ \Omega$ resistor $= 10 \sqrt{2} \ V$
$(D)$ The voltage across $50 \ \Omega$ resistor $= 10 \sqrt{2} \ V$

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$A$ coil is connected to an $AC$ source with peak emf, $8 \, V$ and frequency $\frac{30}{\pi} \, Hz$. The coil has a resistance of $8 \, \Omega$. If the average power dissipated by the coil is $0.4 \, W$, then the inductance of the coil is (in $, H$)

MediumTS EAMCET 2019

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