(D) The initial impedance is $Z = \sqrt{R^2 + X_c^2}$,where $X_c = \frac{1}{\omega C}$. The initial current is $I = \frac{V}{Z}$.When the frequency ch

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

(D) The initial impedance is $Z = \sqrt{R^2 + X_c^2}$,where $X_c = \frac{1}{\omega C}$. The initial current is $I = \frac{V}{Z}$.When the frequency changes to $\omega' = \frac{\omega}{3}$,the new reactance is $X_c' = \frac{1}{\omega' C} = \frac{1}{(\omega/3)C} = 3X_c$.The new impedance is $Z' = \sqrt{R^2 + (3X_c)^2} = \sqrt{R^2 + 9X_c^2}$.The new current is $I' = \frac{V}{Z'} = \frac{I}{2}$,which implies $Z' = 2Z$.Squaring both sides,$Z'^2 = 4Z^2$,so $R^2 + 9X_c^2 = 4(R^2 + X_c^2)$.$R^2 + 9X_c^2 = 4R^2 + 4X_c^2$.$5X_c^2 = 3R^2$.$\frac{X_c^2}{R^2} = \frac{3}{5}$.Therefore,the ratio $\frac{X_c}{R} = \sqrt{\frac{3}{5}}$.

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

Difficult

An $a.c.$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\frac{\omega}{3}$ (while maintaining the same voltage),the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\omega$ is:

MHT CET 2021 All MHT CET

A
$\sqrt{\frac{2}{5}}$
B
$\sqrt{\frac{1}{5}}$
C
$\sqrt{\frac{4}{5}}$
D
$\sqrt{\frac{3}{5}}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Alternating Current

Subtopic

RL, RC and LC AC Circuits

Previous Year

MHT CET 2021 Paper All MHT CET years →

In a series $A.C.$ circuit,the current and voltage are given respectively as:
$I = 10 \sin \omega t$; $V = 10 \sin \left( \omega t + \pi / 4 \right)$
Then,which of the following elements may be present in the circuit?
$(a)$ Only $C$
$(b)$ All $L, C$ and $R$
$(c)$ Both $C$ and $R$
$(d)$ Both $L$ and $R$

Medium

View Solution

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 . . . . . . .

EasyAP EAMCET 2017

View Solution

In an $L-C-R$ circuit,the potential difference across the inductor is $60\,V$,across the capacitor is $30\,V$,and across the resistor is $40\,V$. The supply voltage will be: (in $,V$)

Difficult

View Solution

An inductance coil has a resistance of $80 \Omega$. When an $AC$ signal of frequency $480 \text{ Hz}$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=1 / \sqrt{2}\right]$

MediumMHT CET 2024

View Solution

An electric bulb rated $100 \,W - 300 \,V$ is connected to an $AC$ supply of $500 \,V$ and $\frac{150}{\pi} \,Hz$. The required inductance to save the electric bulb is .......... $H$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

In a series $A.C.$ circuit,the current and voltage are given respectively as:$I = 10 \sin \omega t$; $V = 10 \sin \left( \omega t + \pi / 4 \right)$Then,which of the following elements may be present in the circuit?$(a)$ Only $C$$(b)$ All $L, C$ and $R$$(c)$ Both $C$ and $R$$(d)$ Both $L$ and $R$

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 . . . . . . .

In an $L-C-R$ circuit,the potential difference across the inductor is $60\,V$,across the capacitor is $30\,V$,and across the resistor is $40\,V$. The supply voltage will be: (in $,V$)

An inductance coil has a resistance of $80 \Omega$. When an $AC$ signal of frequency $480 \text{ Hz}$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=1 / \sqrt{2}\right]$

An electric bulb rated $100 \,W - 300 \,V$ is connected to an $AC$ supply of $500 \,V$ and $\frac{150}{\pi} \,Hz$. The required inductance to save the electric bulb is .......... $H$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module