A capacitor and a resistor of resistance 100 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(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 $50 \mu 	ext{F}$.

Similar Questions

In a series $L-C-R$ circuit,

In an $LR$ circuit,the value of $L$ is $(\frac{0.3}{\pi}) \ H$ and the value of $R$ is $40 \ \Omega$. If an alternating e.m.f. of $230 \ V$ at $50 \ Hz$ is connected to the circuit,what are the impedance and the current in the circuit,respectively?

An alternating current of frequency $f$ is flowing in a circuit containing a resistance $R$ and a choke $L$ in series. The impedance of this circuit is

For a series $LCR$ circuit,which one of the following is a $CORRECT$ statement?

In an $A.C.$ circuit,a resistance '$R$' is connected in series with an inductance '$L$'. If the phase angle between voltage and current is $45^{\circ}$,the value of inductive reactance will be $(\tan 45^{\circ} = 1)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module