Embibe Experts Solutions for Exercise 1: ICSE-2018

An ac generator generating an emf of $\epsilon =300 \sin \left(100\pi t\right) V$ is connected to a series combination of $16 \mu F$ capacitor, $1H$ inductor and $100 \Omega$ resistor. Calculate the Resonant frequency.

An ac generator generating an emf of $\epsilon =300 \sin \left(100\pi t\right) V$ is connected to a series combination of $16 \mu F$ capacitor, $1H$ inductor and $100 \Omega$ resistor. Calculate the power factor at resonant frequency.

Draw a labelled graph showing the variation of inductive reactance $\left(X_L\right)$ verses frequency $\left(f\right)$.

State any two characteristics of resonance in an $LCR$ series circuit.

Draw a labelled graph showing the variation of impedance $\left(Z\right)$ of a series LCR circuit versus frequency $\left(f\right)$ of an ac supply.

When an alternating emf $e=310 \sin \left(100\pi t\right)V$ is applied to a series $LCR$ circuit, the current flowing through it is $i=5 \sin \left(100\pi t+\pi /3\right) \mathrm{A}$. What is the phase difference between the current and the emf?

When an alternating emf $e=310 \sin \left(100\pi t\right)V$ is applied to a series $LCR$ circuit, the current flowing through it is $i=5 \sin \left(100\pi t+\pi /3\right) \mathrm{A}$. Calculate the average power consumed by the circuit.

Obtain an expression for the resonant frequency $\left(f_o\right)$ of a series LCR circuit.