First slide

Phasors and Phasor Diagrams

Question

A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source of 200 volt, 100 Hz, is connected across the coil, the current in the coil will be :

Easy

A

2.0 A
B

4.0 A
C

8.0 A
D

$\frac{20}{\sqrt{13}} A$

Solution

At 50 Hz, R = 30 $Ω$ , X_L = $ω$ L = 20 $Ω$
At 100 Hz, R = 30 $Ω$ , X'_L = $ω$ ' L = 40 $Ω$
Impedance Z = $\sqrt{R^{2} + X {'_{L}}^{2}} = \sqrt{30^{2} + 40^{2}} = 50 Ω$
Current I = $\frac{V}{Z} = \frac{200}{50} = 4 A$

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