Embibe Experts Solutions for Chapter: Alternating Current, Exercise 1: Manipur Board-2018

What is $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ value of a.c.?

An applied $\mathrm{e}.\mathrm{m}.\mathrm{f}.$ signal consists of superposition of a d.c. source and a.c. source of high frequency. The circuit consists of an inductor $\mathrm{L}$ and a capacitor $\mathrm{C}$ in series. Show that d.c. signal appears across $\mathrm{C}$ and a.c. signal appears across $\mathrm{L}$.

How does the $\mathrm{L}-\mathrm{C}$ circuit produce oscillation? Explain.

Find the reactance of a capacitor having a capacitance $0.5\mathrm{\mu F}$ at $100 \mathrm{Hz}$.

A series LCR circuit with $\mathrm{R}=1 \mathrm{k\Omega }, \mathrm{L}=1.0 \mathrm{mH}, \mathrm{C}=0.001 \mathrm{\mu F}$ is connected to a sinusoidal voltage of peak value $200\sqrt{2}\mathrm{V}$. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one cycle.

Give any two reasons for small energy losses in transformer and write how these can be minimised.

A sinusoidal voltage of peak value $230\sqrt{2}\mathrm{V}$ with variable frequency is applied to a series LCR circuit in which $\mathrm{R}=5\mathrm{\Omega }, \mathrm{L}=\frac{250}{\mathrm{\pi }}\mathrm{mH}$ and $\mathrm{C}=\frac{400}{\mathrm{\pi }}\mathrm{\mu F}$.

$\left(\mathrm{a}\right)$ Find the frequency of the source at which resonance occurs.

A sinusoidal voltage of peak value $283\mathrm{V}$ with variable frequency is applied to a series LCR circuit in which $\mathrm{R}=3\mathrm{\Omega }, \mathrm{L}=25.48\mathrm{mH}$ and $\mathrm{C}=786\mathrm{\mu F}$

$\left(\mathrm{b}\right)$ Calculate the impedance, the $\mathrm{r}.\mathrm{m}.\mathrm{s}.$ current and the power dissipated at resonance condition.