Question

A coil of inductance 100 mH and unknown resistance and a 1.1 μF capacitor are connected in series with an alternating emf of frequency 800 Hz. If the phase constant between the applied voltage and the current is 74°, what is the resistance of the coil?

Answer 1

Answer:

51.8720 ohm

Explanation:

We have given inductance $L=100mH=100\times 10^{-3}H$

Frequency of the emf is f=800 Hz

So $X_L=\omega L=2\pi f\times L=2\times 3.14\times 800\times 10^{-5}=0.05024ohm$

Capacitance $C=1.1\mu F=1.1\times 10^{-6}F$

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\frac{1}{2\times 3.14\times 800\times 1.1\times 10^{-6}}=180.9496ohm$

We know that $tan\Phi =\frac{X_C-X_L}{R}$

$tan\74 =\frac{180.9496-0.05024}{R}$

$3.4874 =\frac{180.9496-0.05024}{R}$

$R=51.8720ohm$