S. L. Arora Solutions for Chapter: Alternating Current and Electrical Machines, Exercise 5: Problems For Practice

A capacitor, resistor of $5\mathrm{\Omega }$, and an inductor of $50\mathrm{}\mathrm{m}\mathrm{H}$ are in series with an a.c. source marked $100\mathrm{}\mathrm{V},\mathrm{}50\mathrm{}\mathrm{H}\mathrm{z}$. It is found that voltage is in phase with the current. Calculate the capacitance of the capacitor and the impedance of the circuit.

In the a.c. circuit shown in figure, the main supply has constant voltage but variable frequency. For what frequency will the voltage across the resistance $R$ be maximum?

An a.c Source of frequency $50$ hertz is connected to a $50 \mathrm{m}\mathrm{H}$ inductor and a bulb. The bulb glows with some brightness. Calculate the capacitance of the capacitor to be connected in series with the circuit, so that the bulb glows with maximum brightness.

A $200\mathrm{}\mathrm{k}\mathrm{m}$ long telegraph wire has a capacity of $0.014\mu \mathrm{F}$ per $\mathrm{k}\mathrm{m}$. If it carries an alternating current of $50\mathrm{}\mathrm{k}\mathrm{H}\mathrm{z},$ what should be the value of an inductance required to be connected in series so that impedance is minimum? Take $\pi =\sqrt{10}$.

A series $LCR$ circuit with $\mathrm{L}\mathrm{}=\mathrm{}4.0\mathrm{}\mathrm{H}$, $\mathrm{C}\mathrm{}=\mathrm{}100\mathrm{}\mathrm{\mu }\mathrm{}\mathrm{F}$ and $R=60\mathrm{\Omega }$ is connected to a variable frequency $240\mathrm{}\mathrm{V}$ source as shown in Figure.

(i) The angular frequency of the source which drives the circuit at resonance

(ii) The current at the resonating frequency

(iii) The rms potential drop across the inductor at resonance

A series $\mathrm{L}\mathrm{C}\mathrm{R}$-circuit is connected to an ac source $(200\mathrm{}\mathrm{V},\mathrm{}50\mathrm{}\mathrm{H}\mathrm{z}).$ The voltages across the resistor, capacitor and inductor are respectively $200\mathrm{}\mathrm{V},\mathrm{}250\mathrm{}\mathrm{V}$ and $250\mathrm{}\mathrm{V}$.

(i) The algebraic sum of the voltages across the three elements is greater than the voltage of the source. How is this paradox resolved?

(ii) Given the value of the resistance $R$ is $40\mathrm{\Omega },$calculate the current in the circuit.

An inductor of $200\mathrm{}\mathrm{m}\mathrm{H},$ capacitor of $400\mathrm{}\mathrm{\mu }\mathrm{F}$ and a resistor of $10\mathrm{}\mathrm{\Omega }$ are connected in series to an a.c. source of $50\mathrm{}\mathrm{V}$ of variable frequency. Calculate:

(i) the angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and
(ii) the value of Q-factor in the circuit.

A sinusoidal voltage of peak value $10\mathrm{}\mathrm{V}$ is applied to a series $LCR$-circuit in which resistance, capacitance and inductance have values of $10\mathrm{\Omega },1\mu \mathrm{F}$ and $1\mathrm{}\mathrm{H}$ respectively. Find (i) the peak voltage across the inductor at resonance (ii) quality factor of the circuit.