First slide

Phasors and Phasor Diagrams

Question

When an inductor and resistor (R) are connected in series, and the combination is connected to a 200 volt, 50 Hz A.C. supply, the phase difference between the current and voltage is found to be $60^{o}$ . If the resistance of the resistor is 50 $Ω$ , the rms value of current in the circuit is

Moderate

A

4 A
B

2.5 A
C

$3 \sqrt{2} A$
D

2 A

Solution

$\begin{array}{l} \frac{X_{L}}{R} = \tan 60^{ο} \Rightarrow X_{L} = \sqrt{3} R \\ ∴ Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{R^{2} + {(\sqrt{3} R)}^{2}} = 2 R = 100 Ω \\ ∴ I_{r m s} = \frac{V}{2} = \frac{200}{100} A = 2 A \end{array}$

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