A capacitor and a resistor of resistance 100 | vedclass

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(B) Given: Resistance $R = 100 \sqrt{3} \Omega$,Voltage $V = 100 \sin(200t) 	ext{ V}$,Phase difference $\phi = 30^{\circ}$.Comparing the voltage equa

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$50$

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(B) Given: Resistance $R = 100 \sqrt{3} \Omega$,Voltage $V = 100 \sin(200t) 	ext{ V}$,Phase difference $\phi = 30^{\circ}$.Comparing the voltage equation with $V = V_m \sin(\omega t)$,we get angular frequency $\omega = 200 	ext{ rad/s}$.In an $RC$ series circuit,the phase difference $\phi$ is given by $	an \phi = \frac{X_C}{R}$,where $X_C = \frac{1}{\omega C}$.Substituting the values: $	an 30^{\circ} = \frac{1}{\omega C R}$.Since $	an 30^{\circ} = \frac{1}{\sqrt{3}}$,we have $\frac{1}{\sqrt{3}} = \frac{1}{200 	imes C 	imes 100 \sqrt{3}}$.Canceling $\sqrt{3}$ from both sides: $1 = \frac{1}{200 	imes 100 	imes C}$.$C = \frac{1}{20000} 	ext{ F} = 0.5 	imes 10^{-4} 	ext{ F} = 50 	imes 10^{-6} 	ext{ F} = 50 \mu 	ext{F}$.Thus,the capacitance is $50 \mu 	ext{F}$.

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