A resistor of 20 Omega and a capacitor are c | vedclass

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

Question

(B) The phase angle $\phi$ in an $RC$ series circuit is given by $	an(\phi) = \frac{X_C}{R}$.Given $\phi = 30^\circ$,$R = 20 \ \Omega$,and $f = 50 \

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{2 \pi} \ mF$

Vedclass · Answer

(B) The phase angle $\phi$ in an $RC$ series circuit is given by $	an(\phi) = \frac{X_C}{R}$.Given $\phi = 30^\circ$,$R = 20 \ \Omega$,and $f = 50 \ Hz$.$	an(30^\circ) = \frac{1}{\sqrt{3}} = \frac{X_C}{20}$.Therefore,$X_C = \frac{20}{\sqrt{3}} \ \Omega$.Since $X_C = \frac{1}{2 \pi f C}$,we have $\frac{1}{2 \pi 	imes 50 	imes C} = \frac{20}{\sqrt{3}}$.$\frac{1}{100 \pi C} = \frac{20}{\sqrt{3}}$.Solving for $C$: $C = \frac{\sqrt{3}}{2000 \pi} \ F$.To convert to $mF$ (millifarads),multiply by $10^3$: $C = \frac{\sqrt{3}}{2000 \pi} 	imes 10^3 \ mF = \frac{\sqrt{3}}{2 \pi} \ mF$.

$A$ resistor of $20 \ \Omega$ and a capacitor are connected in series with an $AC$ current source of $50 \ Hz$. What should be the capacitance to produce a phase difference of $30^\circ$ between the voltage and current?

Similar Questions

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .

$A$ coil of negligible resistance is connected in series with a $90 \Omega$ resistor across a $120 \text{ V}, 60 \text{ Hz}$ supply. $A$ voltmeter reads $36 \text{ V}$ across the resistor. The inductance of the coil is: (in $\text{ H}$)

$A$ coil has self-inductance $L = 0.04 \ H$ and resistance $R = 12 \ \Omega$. When it is connected to a $220 \ V, 50 \ Hz$ supply,what will be the current flowing through the coil (in $A$)?

In an $ac$ circuit,the potential difference across an inductance and resistance joined in series are respectively $16\, V$ and $20\, V$. The total potential difference across the circuit is.......$V$

An electric bulb and a capacitor are connected in series with an $AC$ source. On increasing the frequency of the source,the brightness of the bulb

Vedclass Test Series

Exam Paper Generator

Online Exam Module