Question

An inductor and a bulb are connected in series to an ac source of 220v and 50hz.A current of 11a

Answer 1

Given that,

Voltage of source $V_{rms}= 220 V$

Frequency = 50 Hz

Current $I_{rms}= 11\ A$

Suppose, A current of 11 A flows in the circuit the phase angle between voltage and current is 45 degree .Calculate  the impedance and inductance of the circuit.

We know that,

The impedance is

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

We need to calculate the resistance

Using formula of impedance

$R=\dfrac{V_{rms}}{I_{rms}}$

Put the value into the formula

$R=\dfrac{220}{11}$

$R=20\ \Omega$

We need to calculate the $X_{L}$

Using formula of $X_{L}$

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

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

Put the value into the formula

$X_{L}=R\times\tan\dfrac{\pi}{4}$

$X_{L}=R\times 1$

$X_{L}=R$

Put the value of R and $X_{L}$

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

$Z=\sqrt{2}R$

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

Put the value into the formula

$R=\dfrac{20}{\sqrt{2}}$

$R=14.14\ \Omega$

We need to calculate the inductance

Using formula of inductance

$2\pi fL=R$

$L=\dfrac{R}{2\pi f}$

Put the value into the formula

$L=\dfrac{14.14}{2\pi\times50}$

$L=0.045\ Henry$

Hence, The impedance and inductance are 14.14 ohm and 0.045 Henry