Embibe Experts Solutions for Chapter: Alternating Current, Exercise 4: Exercise-4

An alternating current is given by $I=I_2\cos \omega t+I_2\sin \omega t$. Calculate its $\mathrm{rms}$ value.

The current and voltage in a circuit is given by $i=3.5 \sin \left(628 t+30°\right) \mathrm{A}, \mathrm{V}=28\sin \left(628\mathrm{t}-30°\right) \mathrm{volt}$

Find

(i) time period current

(ii) phase difference between voltage and current.

An inductance coil has a resistance of $100 \mathrm{ohm}$. When a.c. signal of frequency $1000\mathrm{}\mathrm{H}\mathrm{z}$ is applied to the coil, the applied voltage leads the current by $45°$. Calculate the self-inductance of the coil.

The given graphs $\left(A\right)$ and $\left(B\right)$ represent the variation the opposition offered by the circuit element to the flow of alternating current, with frequency of the applied emf. Identify the circuit element corresponding to each graph.

A choke coil of resistance $R$ and inductance $L$ is connected in series with capacitor $C$ and complete combination is connected to $\mathrm{a}.\mathrm{c}.$ voltage, Circuit resonates when angular frequency of supply is $\omega ={\omega }_0$.

(i) Find out relation between ${\omega }_0, L$ and $C$

(ii) What is phase difference between $V$ and $I$ at resonance, is it changes when resistance of choke coil is zero.

In a series $\mathrm{LCR}$ circuit as shown in figure

Calculate the impedance, current flow in the circuit, the heat developed.