Question

A source of 220V is applied in an A.C. circuit. The value of resistance is 220Ω. Frequency & inductance are 50 Hz and 0.7 H, then wattles current is
A. 0.5amp
B. 0.7amp
C. 1.0amp
D. none

Answer 1

Here we should understand the concept of wattles current and we need to calculate the inductance by using the formula. Then we get a solution for this problem.

Complete step by step answer:
Given:
$R = 2\Omega$
${V_{rms}} = 220V$
${V_0} = 220\sqrt 2$V
Calculating the inductance,
${X_L} = \omega L$
=$100\pi \times 0.7$
=220Ω
Therefore the impedance is Z= 200$\sqrt 3$
Also tanϕ=$\dfrac{{{V_L}}}{R}$=1
ϕ=45 degree
Hence wattles current is
=${i_0}\sin \phi$
=$\dfrac{{220\sqrt 3 }}{{220\sqrt 2 }}\sin {45^0}$
= 0.7A
Hence the correct option is B.

Additional information: In a capacitor, when the current is flowing through a capacitor and the potential difference across the capacitor varies 90 degrees which is out of phase. Hence, it can also say that the current which is leading the voltage is lagging by 90 degrees.
In the inductor, when the current is flowing through an inductor and the potential difference across the inductor varies 90 degrees which is out of phase. Hence, it can also say that the voltage is leading and the current is lagging by 90 degrees.

Note: An AC circuit containing either capacitor or inductor current is said to wattles if the average power consumed in the circuit is zero. The formula used for calculating the wattles current is:
P = IV sinӨ
Where,
P is the power in Watts
I is the current in Amperes
V is the voltage in Volts
sinӨ is the angular phase difference between the current and voltage