Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 9

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Series resonance Quality factor

Series Resonance Quality Factor

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Q: 21. Obtain the resonant frequency and of a series of a series LCR circuit with. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of. Suggest a suitable way.

Answer:

Inductance,

Capacitance,

Resistance,

At resonance, angular frequency of the source for the given LCR series circuit is given as:

Q-factor of the series:

To improve the sharpness of the resonance by reducing its ‘full width at half maximum’ by a factor of without changing, we need to reduce R to half i.e.,

Resistance

Q: 22. Answer the following questions:

(A) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?

(B) A capacitor is used in the primary circuit of an induction coil.

(C) An applied voltage signal consists of a superposition of a dc voltage and an voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.

(D) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an line.

(E) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?

Answer:

(A) Yes; the statement is not true for rms voltage

It is true that in any ac circuit, the applied voltage is equal to the average sum of the instantaneous voltages across the series elements of the circuit. However, this is not true for rms voltage because voltages across different elements may not be in phase.

(B) High induced voltage is used to charge the capacitor. A capacitor is used in the primary circuit of an induction coil. This is because when the circuit is broken, a high induced voltage is used to charge the capacitor to avoid sparks.

(C) The dc signal will appear across capacitor C because for dc signals, the impedance of an inductor (L) is negligible while the impedance of a capacitor (C) is very high (almost infinite). Hence, a dc signal appears across C. For an signal of high frequency, the impedance of L is high and that of C is very low. Hence, an signal of high frequency appears across L.

(D) If an iron core is inserted in the choke coil (which is in series with a lamp connected to the ac line), then the lamp will glow dimly. This is because the choke coil and the iron core increase the impedance of the circuit.

(E) A choke coil is needed in the use of fluorescent tubes with ac mains because it reduces the voltage across the tube without wasting much power. An ordinary resistor cannot be used instead of a choke coil for this purpose because it wastes power in the form of heat.

Q: 23. A power transmission line feeds input power at to a step-down transformer with its primary windings having turns. What should be the number of turns in the secondary in order to get output power at?

Answer:

Input voltage,

Number of turns in primary coil,

Output voltage,

Number of turns in secondary coil

Voltage is related to the number of turns as:

Hence, there are turns in the second winding.

Q: 24. At a hydroelectric power plant, the water pressure head is at a height of and the water flow available is. If the turbine generator efficiency is estimate the electric power available from the plant.

Answer:

Height of water pressure head,

Volume of water flow per second,

Efficiency of turbine generator,

Acceleration due to gravity,

Density of water,

Electric power available from the plant