First slide

Phasors and Phasor Diagrams

Question

An inductive coil and resistance of $100 Ω$ . When an ac signal of frequency 1000 Hz is fed to the coil, the applied voltage leads the current by $45^{o}$ . What is the inductance of the coil?

Easy

A

2 mH
B

3.3 mH
C

16 mH
D

$\sqrt{5}$ mH

Solution

$\frac{V_{L}}{V_{R}} = tanΦ = \tan 45^{o} = 1$
$\frac{Lω}{R} = 1$
$L = \frac{R}{ω} = \frac{100}{2 π \times 1000} = \frac{1}{20 π} = \frac{1}{62 .8} = \frac{1000}{62 .8} \times 10^{- 3} = 16 mH$

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