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 = 50Hz)

Moderate

A

0.052 H
B

2.42 H
C

16.2 mH
D

1.62 mH

Solution

Current through the bulb
$i = \frac{P}{V} = \frac{{60}}{{10}} = 6A$
$V = \sqrt {V_R^2 + V_L^2}$
${(100)^2} = {(10)^2} + V_L^2 \Rightarrow \,\,{V_L} = 99.5\,\,Volt$
$Also\,\,{V_L} = i{X_L} = i \times (2\pi \nu L)$
$\Rightarrow \,99.5 = 6 \times 2 \times 3.14 \times 50 \times L \Rightarrow \,\,L = 0.052\,\,H$

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