Question

32. An inductance of 0.4 Henry and a resistance of 100ohm are connected to a A.C. voltage source of 220V and 50 Hz. Then find out the phase differencebetween the voltage and current flowing in thecircuit :(1) tan-1 (2.25 T) (2) tan-1 (0.4 T)(3) tan-1 (1.57) (4) tan-1 (0.5 T)​

Answer 1

The phase difference between the voltage and current is $\tan^{-1}(1.25)$

This value is near by option C.

Explanation:

Given that,

Inductance = 0.4 Henry

Resistance = 100 ohm

Voltage = 220 V

Frequency = 50 Hz

We need to calculate the phase difference between the voltage and current

Using formula of phase angle

$\tan\theta=\dfrac{\omega\times L}{R}$

$\theta=\tan^{-1}(\dfrac{\omega\times L}{R})$

$\theta=\tan^{-1}(\dfrac{2\pi\times f\times L}{R})$

Where, $\omega$=angular frequency

L = inductance

R = resistance

Put the value into the formula

$\theta=\tan^{-1}(\dfrac{2\pi\times50\times0.4}{100})$

$\theta=\tan^{-1}(1.25)$

Hence, The phase difference between the voltage and current is $\tan^{-1}(1.25)$

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Topic : phase angle

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