ASSIGNMENT ALTERNATING CURRENT CLASS XII

1. Prove that an ideal capacitor in an a.c. circuit does not dissipate power.
2. Prove that an ideal inductor does not dissipate any power in an a.c. circuit.
3. An a.c. source generating a voltage v = v m sinωt is connected to a capacitor of
capacitance C. find the expression for the current i flowing through it. Plot a graph of v
and i versus ωt to show that the current is π/2 ahead of the voltage. A resistor of 200 Ω
and a capacitor of 15 µF are connected in series to a 220 V, 50 Hz a.c. source. Calculate the
current in the circuit and the rms voltage across the resistor and the capacitor. Is the
algebraic sum of these voltages more than the source voltage? If yes, solve the paradox.
4. Explain, briefly, with the help of a labelled diagram, the basic principle of the working
of an a.c. generator. In an a.c generator, coil of N turns and area A is rotated at ʋ
revolutions per second in a uniform magnetic field B. Write the expression for emf produced.
A 100 turn coil of area 0.1 m 2 rotates at half a revolution per second. It is placed in a
magnetic field 0.01 T perpendicular to the axis of rotation of the coil. Calculate the
maximum voltage generated in the coil.
5. (i) Derive an expression for the average power consumed in a series LCR circuit connected
to a.c. source in which the phase difference between the voltage and the current in the
circuit is Φ. (ii) Define the quality factor in a.c. circuit. Why should the quality factor
have high value in receiving circuits? Name the factors on which it depends.
6. Derive the relationship between the peak and the rms value of current in an a.c. circuit.
7. Describe briefly, with the help of a labelled diagram, working of a step up transformer. A
step up transformer converts a low voltage into high voltage. Does it not violate the
principle of conservation of energy? Explain.
8. Mention the two characteristic properties of the material suitable for making core of a
transformer.
9. (i) When a a.c. source is connected to an ideal capacitor show that the average power
supplied by the source over a complete cycle is zero. (ii) A lamp is connected in series with
a capacitor. Predict your observations when the system is connected first across a d.c. and
then an a.c source. What happens in each case if the capacitance of the capacitor is reduced?
10. An inductor L of inductance X L is connected in series with a bulb B and an ac
source. How would brightness of the bulb change when (i) number of turns in the
inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a
capacitor of reactance X c = X L is inserted in series in the circuit. Justify your
answer in each case.