Question

A source of 220V and 40Hz is connected to a series of 6Ω resistor, 0.01 H inductor.
Calculate the phase angle and power factor of the circuit.

Answer 1

Answer:

(a). The phase angle is 22.72°.

(b). The power factor is 0.92.

Explanation:

Given that,

Voltage = 220 V

Frequency = 40 Hz

Resistance = 6 Ω

Inductance = 0.01 H

We need to calculate the angular frequency

$\omega=2\pi\neu$

Put the value into the formula

$\omega=2\times\pi\times40$

$\omega=251.32\ rad/sec$

We need to calculate the inductive reactant

Using formula of inductive reactant

$X_{l}=\omega\times L[/tezx]</p><p>Put the value into the formula</p><p>[tex]X_{L}=251.32\times0.01$

$X_{L}=2.513\ \Omega$

We need to calculate the total impedance

Using formula of impedance

$z=\sqrt{R^2+X_{L}^2}$

Put the value into the formula

$z=\sqrt{6^2+(2.513)^2}$

$z=6.5\ \Omega$

We need to calculate the phase angle

Using formula of phase angle

$\tan\phi=\dfrac{X_{L}}{R}$

$\phi=\tan^{-1}\dfrac{X_{L}}{R}$

Put the value into the formula

$\phi=\tan^{-1}\dfrac{2.513}{6}$

$\phi=22.72^{\circ}$

We need to calculate the power factor

Using formula of power factor

$Power\ factor = \cos\phi$

Put the value into the formula

$Power\ factor = \cos22.72$

$Power\ factor =0.92$

Hence, (a). The phase angle is 22.72°.

(b). The power factor is 0.92.