When the frequency of ac supply is such that the inductive reactance and capacitive reactance become equal, the impedance of the series LCR circuit i equal to the ohmic resistance in the circuit. Such a series LCR circuit is known as resonant series LCR circuit and the frequency of the ac supply is known as resonant frequency
Resonance phenomenon is exhibited by a circuit only ifboth Land C are present in the circuit. We cannot have resonance in a RL or RC circuit
A series LCR circuit with \(L=0.12 \mathrm{H}, C=480 \mathrm{nF}, R=23 \Omega\) is connected to a 230 V variable frequency supply

(i) Find the value of source frequency for which current amplitude is maximum

(ii) The value of maximum current is

(iii) The value of maximum power is

(iv) What is the Q-factor of the given circuit?

(v) At resonance which of the following physical quantity is maximum?

An LC circuit also called a resonant circuit, tank circuit or tuned circuit is an electric circuit consisting of an inductor represented by the letter L and a capacitor, represented by the letter C connected together. An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance.
An LC circuit contains a 20 mH inductor and a \(50 \mu \mathrm{F}\) capacitor with an initial charge of 10 mC The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.

(i) The total energy stored initially is

(ii) The natural frequency of the circuit is

(iii) At what time is the energy stored completely electrical?

(iv) At what time is the energy stored completely magnetic?

(v) The value of X_L is

Step-down transformers are used to decrease or step-down voltages. These are used when voltages need to be lowered for use in homes and factories.
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is \(0.5 \Omega\) per km. The town gets power from the line through a 4000 - 220 V step-down transformer at a sub-station in the town.

(i) The value of total resistance of the wires is

(ii) The line power loss in the form of heat is

(iii) How much power must the plant supply, assuming there is negligible power loss due to leakage?

(iv) The voltage drop in the power line is

(v) The total value of voltage transmitted from the plant is

In an a.c. circuit, values of voltage and current change every instant. Therefore, power of an a.c. circuit at any instant is the product of instantaneous voltage (E) and instantaneous current (I). The average power supplied to a pure resistance R over a complete cycle of a.c. is \(P=E_{v} I_{v}\) When circuit is inductive, average power per cycle is \(E_{v} I_{v} \cos \phi\)

In an a.c. circuit, 600 mH inductor and a \(50 \mu \mathrm{F}\) capacitor are connected in series with \(10 \Omega\) nresistance. The a.c. supply to the circuit is 230 V, 60 Hz. 
(i) The average power transferred per cycle to resistance is

(ii) The average power transferred per cycle to capacitor is

(iii) The average power transferred per cycle to inductor is

(iv) The total power transferred per cycle by all the three circuit elements is

(v) The electrical energy spend in running, the circuit for one hour is

A transformer is an electrical device which is used for changing the a.c. voltages. It is based on the phenomenon of mutual induction i.e. whenever the amount of magnetic flux linked with a coil changes, an e.m.f is induced in the neighbouring coil. For. an ideal transformer, the resistances of the primary and secondary windings are negligible.

It can be shown that \(\frac{E_{s}}{E_{p}}=\frac{I_{p}}{I_{s}}=\frac{n_{s}}{n_{p}}=k\)
where the symbols have their standard meanings.
For a step up transformer \(n_{s}>n_{p} ; E_{s}>E_{p} ; k>1 ; \quad \therefore I_{s}
For a step down transformer \(n_{s}
The above relations are on the assumptions that efficiency of transformer is 100%.
lentlac ,effciency \(\eta=\frac{\text { output power }}{\text { intput power }}=\frac{E_{s} I_{s}}{E_{p} I_{p}}\)
(i) Which of the following quantity remains constant in an ideal transformer?

(ii) Transformer is used to

(iii) The number of turns in primary coil of a transformer is 20 and the number of turns in a secondary is 10. If the voltage across the primary is 220 ac V, what is the voltage across the secondary?

(iv) In a transformer the number of primary turns is four times that of the secondary turns. Its primary is connected to an a.c. source of voltage V. Then

(v) A transformer is used to light 100 W-110 V lamp from 220 V mains. If the main current is 0.5 A, the efficiency of the transformer is