A circuit connected to an ac source of emf $e=e_{0} \sin(100 t)$ with t in seconds, gives a phase difference of $\frac{\pi}{4}$ betweeen the emf e and current i. Which of the following circuit will exhibit this?

Option 1)
RL circuit with $R=1 \;k\Omega$ and L=10 mH

Option 2)
RL circuit with $R=1 \;k\Omega$ and L=1 mH

Option 3)
RC circuit with $R=1 \;k\Omega$ and $C=1\mu F$

Option 4)
RC circuit with $R=1 \;k\Omega$ and $C=10\mu F$

Answers (1)

S solutionqc

$w=100^{-1}$

for phase difference of $\frac{\pi}{4}\Rightarrow \left | X_{L}-X_{C} \right |=R$

if $\;X_{C}=0 \Rightarrow X_{L}=R \Rightarrow wL=R \Rightarrow L=\frac{R}{w}$

if $\;X_{L}=0 \Rightarrow X_{C}=R= \frac{1}{wC} \Rightarrow C=\frac{1}{wR}$

for option (4)

$R=1k\Omega$

$C=\frac{1}{wR}=\frac{1}{\frac{100}{5}\times 10^{3} \Omega }= 10^{-5}_{s/ \Omega}\Rightarrow 10 \times 0^{-6}_{s/ \Omega}\Rightarrow 10\mu F$

Option 1)

RL circuit with $R=1 \;k\Omega$ and L=10 mH

Option 2)

RL circuit with $R=1 \;k\Omega$ and L=1 mH

Option 3)

RC circuit with $R=1 \;k\Omega$ and $C=1\mu F$

Option 4)

RC circuit with $R=1 \;k\Omega$ and $C=10\mu F$

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges

Resources

Colleges

Resources

Exams

Exams

Colleges

Predictor

Resources

Exams

Predictors

Resources

Upcoming Events

Exams

Ranking

Products & Resources

NCERT Solutions

Exams

Country

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Predictors

Resources

Engineering Preparation

Government Jobs

Medical Preparation

Exams

Colleges

Predictors

Resources

Resources

Exams

Colleges

Predictors

Exams

Predictors

Colleges

Resources

Exams

Colleges

Resources

Exams

Resources

Similar Questions

Preparation Products

Knockout JEE Main Sept 2020

Rank Booster JEE Main 2020

Test Series JEE Main Sept 2020

Knockout JEE Main April 2021

Knockout JEE Main April 2022

Ask Question

Register to post Answer