First slide

Phasors and Phasor Diagrams

Question

One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has self inductance of value $(f = 50 Hz)$

Moderate

A

0.052 H
B

2.42 H
C

16.2 mH
D

1.62 mH

Solution

Current through the bulb $i = \frac{P}{V} = \frac{60}{10} = 6 A$
$\begin{array}{l} V = \sqrt{V_{R}^{2} + V_{L}^{2}} \\ (100)^{2} = (10)^{2} + V_{L}^{2} \Rightarrow V_{L} = 99.5 Volt \\ Also V_{L} = i X_{L} = i \times (2 π V) \\ \Rightarrow 99.5 = 6 \times 2 \times 3.14 \times 50 \times L \Rightarrow L = 0.052 H \end{array}$

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