Alternating Current · Physics · Class 12

(a) (i) You are given three circuit elements $\mathrm{X}, \mathrm{Y}$ and $Z$. They are connected one by one across a given ac source. It is found that V and I are in phase for element $X$. V leads I by $\left(\frac{\pi}{4}\right)$ for element $Y$ while I leads $V$ by $\left(\frac{\pi}{4}\right)$ for element $Z$. Identify elements X, Y and $Z$.

(ii) Establish the expression for impedance of circuit when elements $X, Y$ and $Z$ are connected in series to an ac source. Show the variation of current in the circuit with the frequency of the applied ac source.

(iii) In a series LCR circuit, obtain the conditions under which (i) impedance is minimum and (ii) wattless current flows in the circuit.

OR

(b) (i) Describe the construction and working of a transformer and hence obtain the relation for $\left(\frac{v_s}{v_p}\right)$ in terms of number of turns of primary and secondary.

(ii) Discuss four main causes of energy loss in a real transformer.

An alternating voltage of $$220 \mathrm{~V}$$ is applied across a device $$X$$. A current of 0.22 A flows in the circuit and it lags behind the applied voltage in phase by $$\pi / 2$$ radian. When the same voltage is applied across another device $$Y$$, the current in the circuit remains the same and it is in phase with the applied voltage.

(i) Name the devices $$X$$ and $$Y$$ and,

(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of $$\mathrm{X}$$ and $$\mathrm{Y}$$.

State the basic principle behind the working of an ac generator. Briefly describe its working and obtain the expression for the instantaneous value of emf induced.

A series CR circuit with $$R=200 \Omega$$ and $$C=(50 / \pi)$$ $$\mu \mathrm{F}$$ is connected across an ac source of peak voltage $$\varepsilon_0=100 \mathrm{~V}$$ and frequency $$v=50 \mathrm{~Hz}$$. Calculate (a) impedance of the circuit $$(\mathrm{Z})$$, (b) phase angle $$(\phi)$$, and (c) voltage across the resistor.

Which of the following statements about a series LCR circuit connected to an ac source is correct?