Question

The power factor in a circuit connected to an $$A.C.$$  The value of power factor is

A. unity when the circuit contains an ideal inductance only
B. unity when the circuit contains an ideal resistance only  
C. zero when the circuit contains an ideal resistance only
D. unity when the circuit contains an ideal capacitance only
Answer :   unity when the circuit contains an ideal resistance only
Solution :
$$\cos \phi = \frac{R}{Z},$$   where $$Z$$ is the impedance & $$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} ,$$      if there is only resistance then $$Z = R \Rightarrow \cos \phi = 1$$

Releted MCQ Question on
Electrostatics and Magnetism >> Alternating Current

Releted Question 1

When an $$AC$$ source of emf $$e = {E_0}\sin \left( {100t} \right)$$    is connected across a circuit, the phase difference between the emf $$e$$ and the current $$i$$ in the circuit is observed to be $$\frac{\pi }{4},$$ as shown in the diagram. If the circuit consists possibly only of $$R - C$$  or $$R - L$$  or $$L - C$$  in series, find the relationship between the two elements
Alternating Current mcq question image

A. $$R = 1k\Omega ,C = 10\mu F$$
B. $$R = 1k\Omega ,C = 1\mu F$$
C. $$R = 1k\Omega ,L = 10H$$
D. $$R = 1k\Omega ,L = 1H$$
Releted Question 2

An $$AC$$  voltage source of variable angular frequency $$\omega $$ and fixed amplitude $${V_0}$$ is connected in series with a capacitance $$C$$ and an electric bulb of resistance $$R$$ (inductance zero). When $$\omega $$ is increase

A. the bulb glows dimmer
B. the bulb glows brighter
C. total impedance of the circuit is unchanged
D. total impedance of the circuit increases
Releted Question 3

In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current in primary coil is $$4A,$$  then that in the secondary coil is

A. $$4 A$$
B. $$2 A$$
C. $$6 A$$
D. $$10 A$$
Releted Question 4

The core of any transformer is laminated so as to

A. reduce the energy loss due to eddy currents
B. make it light weight
C. make it robust and strong
D. increase the secondary voltage

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Alternating Current


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