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#### Question

(i) When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

(ii) A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor? Explain.

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(i) An a.c. source of voltage V = V_{0} sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expression for impedance of a circuit and the phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit, X_{L} = R and power factor of the circuit is P_{1}. When capacitor with capacitance C such that X_{L} = X_{C} is put in series, the power factor becomes P_{2}. Calculate P_{1}/P_{2}

Ajit had a high tension tower erected on his farm land. He kept complaining to the authorities to remove it as it was occupying a large portion of his land. His uncle, who was a teacher, explained to him the need for erecting these towers for efficient transmission of power. As Ajit realised its significance, he stopped complaining.

Answer the following questions:

(a) Why is it necessary to transport power at high voltage?

(b) A low power factor implies large power loss. Explain.

(c) Write two values each displayed by Ajit and his uncle.