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

51.8720 ohm

Step-by-step explanation:

We have given inductance
`L=100mH=100* 10^(-3)H`

Frequency of the emf is f=800 Hz

So
`X_L=\omega L=2\pi f* L=2* 3.14* 800* 10^(-5)=0.05024ohm`

Capacitance
`C=1.1\mu F=1.1* 10^(-6)F`

`X_C=(1)/(\omega C)=(1)/(2\pi fC)=(1)/(2* 3.14* 800* 1.1* 10^(-6))=180.9496ohm`

We know that
`tan\Phi =(X_C-X_L)/(R)`

`tan\74 =(180.9496-0.05024)/(R)`

`3.4874 =(180.9496-0.05024)/(R)`

`R=51.8720ohm`