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.

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.