First slide

Phasors and Phasor Diagrams

Question

When 100 volt DC is applied across a coil, a current of 1 A flows through it. When 100 volt AC at 50 cycles/second is applied to the same coil, only 0.5 ampere current flows. The inductance of the coil is

Moderate

A

$\frac{\sqrt{2}}{π} H$
B

$\frac{\sqrt{3}}{π} H$
C

$\frac{4}{π} H$
D

$\frac{5}{π} H$

Solution

When DC is supplied, $R = \frac{V}{i} = \frac{100}{1} = 100 Ω$
When AC is supplied, $Z = \frac{V}{i} = \frac{100}{0 .5} = 200 Ω Now R^{2} + {X_{L}}^{2} = Z^{2} \Rightarrow X_{L} = \sqrt{200^{2} - 100^{2}} Ω = 100 \sqrt{3} Ω Therefore L = \frac{100 \sqrt{3}}{100 π} H = \frac{\sqrt{3}}{π} Ω$

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