Question

7.When a series combination of inductance and resistance are connected with a 10V, 50 Hz a.c. source, a currentof 1A flows in the circuit. The voltage leads the current by a phase angle of radian. Calculate the valuesof resistance and inductive reactance.​

Answer 1

Answer:

the voltage bleads the current by a phase anhle of radian . calculate the valuesof resistance and inductive reactance . whean a series combination of inductance and resistance

Answer 2

The inductance and resistance are 27.5 mH and 5 ohm.

Explanation:

Given that,

Voltage = 10 V

Frequency = 50 Hz

Current = 1 A

Suppose the phase angle is $\dfrac{\pi}{3}$.

We need to calculate the impedance

Using formula of impedance

$Z=\sqrt{R^2+X_{l}^2}$...(I)

$Z=\sqrt{\dfrac{V}{I}}$

Put the value into the formula

$Z=\sqrt{\dfrac{10}{1}}$

$Z=10\ \Omega$

We need to calculate the inductance

Using formula of inductance

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

Put the value of angle

$\tan\dfrac{\pi}{3}=\dfrac{X_{l}}{R}$

$\sqrt{3}=\dfrac{X_{l}}{R}$

$X_{l}=R\sqrt{3}$....(II)

Put the value of inductance in the equation (I)

$Z=\sqrt{R^2+3R^2}$

$Z=2R$

$R=\dfrac{Z}{2}$

Put the value of Z

$R=5\ \Omega$

Put the value of R in the equation (II)

$X_{l}=5\sqrt{3}$

We need to calculate the value of inductance

Using formula of inductance

$X_{l}=2\pi f L$

$L=\dfrac{X_{l}}{2\pi f}$

Put the value into the formula

$L=\dfrac{5\sqrt{3}}{2\pi\times50}$

$L=0.0275\ H$

$L=27.5\ mH$

Hence, The inductance and resistance are 27.5 mH and 5 ohm.

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Topic : Inductive reactance

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