Questions - Answers
Very Short Answer type Questions
1. A transformer converts 200 V ac into 2000 V ac, calculate the number of turns in the secondary if the primary has 10 turns.
A: VP = 200 Vac ; VS = 2000 Vac; NP = 10 turns; NS = ?
NS = 100 turns.
2. What type of transformer is used in the 6 V bed lamp?
A: The step down transformer is used.
3. What is the phenomenon involved in the working of a transformer?
A: The phenomenon of mutual induction is involved between primary and secondary coil of the transformer.
4. What is transformer ratio?
A: The ratio of output emf to the input emf of a transformer is called transformer ratio i.e. E2/ E1 (or) the ratio of number of turns in the secondary coil to the number of turns in the primary coil is called transformer ratio i.e. N2/N1.
5. Write the expression for the reactance of
(i) An inductor and (ii) A capacitor.
A: (i) Inductive reactance XL = ωL
6. Define power factor? On which factors does power factor depend?
A: The ratio between the average power (Pav) and the current apparent power (Pap = ERMS IRMS) is called the power factor.
7. What is meant by wattless component of a current?
A: When the phase difference between voltage & current is π/2, cos φ = 0 and power P = 0 even though a current is flowing in the circuit. This current is called wattless component of current.
8. What does a LCR series circuit have minimum impendance?
A: 1) When curent is maximum.
2) At resonant frequency,
LCR series have minimum impedance.
9. What is the phase difference between voltage & current when they are power factor in LCR series circuit in unity?
A: At resonance frequency, the phase difference between voltage & current is 0°. The power factor, Cos φ is unity.
Short Answer type Questions
1. Obtain an expression for the current through an inductor when an AC emf is applied.
A: 1) Consider a pure inductor of inductance L. Let the alternating emf of instantaneous value E = E0 Sin ωt be applied to the inductor.
2) Let the instantaneous current at anytime 't' is 'I'.
Where k is a constant of integration. As the average value of 'I' over one cycle is zero, which gives the value of k = 0
6) The instantaneous current through the inductor is,
This is the expression for instantaneous current through a circuit consisting of a pure inductor.
2. Obtain an expression for the current in a capacitor when an A.C. emf is applied.
A: 1) Consider a capacitor 'C'. Let an alternating emf of instantaneous value, E = E0 sin ωt be applied to the capacitor, due to this an AC flows through the capacitor.
2) Let the instantaneous current at anytime 't' is I through the capacitor, 'q' is the charge on the capacitor at that 't'.
4) Differentiating it w.r.t time.
3. State the principle on which a transformer works. Describe the working of a transformer with necessary theory.
A: Principle: A transformer works on the principle of 'Mutual Induction'. Transformer is a device used to transform low voltage high current to high voltage low current and vice versa.
Construction:
1) A transformer consists of two insulated mutually coupled coils of wire wound on a continuous iron core.
2) One of the coil is called "Primary Coil" and the other one "Secondary Coil". The primary 'P' is connected to a source of emf and the secondary to a load.
3) The core is made of closed rectangular steel laminates assembled, to provide a continuous magnetic paths.
Working:
1) When AC passes through the primary, an alternate magnetic field is formed in core.
2) Due to alternating flux linkage an emf is induced in secondary. This is due to mutual induction.
Theory:
1) let N1 and N2 be the number of turns in the primary and the secondary. E1 and E2 be the induced emf's in the primary and secondary respectively.
3) If N2 > N1, the transformer is a step-up transformer, shown in fig (a).
If N2< N1, the transformer is a step-down transformer, shown in fig (b).
4) The efficiency of a transformer is the ratio of Output power to Input power.
Long Answer type Questions
1. Obtain an expression for impedance and current in series LCR circuit. Deduce an expression for the resonating frequency of an LCR series resonating circuit.
A: 1) Consider a circuit containing inductance 'L', capacitance 'C' & resistance 'R' in series.
2) Let an alternating e.m.f. E = E0 Sin ωt be applied to a circuit containing a resistor R, a capacitor capacitance C and an inductor of inductance I connected in series as shown in figure.
3) Let I be the current, q be the charge at any instant t.
11) The frequency response curve LCR circuit is as shown in fiugure. It shows that current is maximum at resonant frequency f0.
Problems
2. In a series LCR circuit R = 200 W and the voltage and the frequency of the mains supply is 200V and 50 Hz respectively. On taking out the capacitance from the circuit behind the current lags behind the voltage by 45°. On taking out the inductor from the circuit the current leads the voltage by 45°. Calculate the power dissipated in the LCR circuit.
A: Given V = 200 V; R = 200 Ω
Power dissipated in the LCR circuit
2. A 100 Ω resistor is connected to a 220 V, 50 Hz a.c. supply.
(a) What is the rms value of current in the circuit?
(b) What is the netpower consumed over a full cycle?
A: EV = 220 V ; R = 100 Ω ; F = 50 Hz.
(b) Power consumed over a full cycle = (IV)2 = R = (2.2)2 × 100 = 484 W.
3. a) The peak voltage of an ac supply is 300 V. What is the rms voltage?
(b) The rms value of current in an a.c. circuit is 10 A. What is the peak current?
