First slide

Phasors and Phasor Diagrams

Question

A virtual current of 4 A and 50 Hz flows in an AC circuit containing a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V its inductance will be

Difficult

A

$\frac{1}{3 π} H$
B

$\frac{1}{5 π} H$
C

$\frac{1}{7 π} H$
D

$\frac{1}{9 π} H$

Solution

$I V \cos φ = P \Rightarrow 4 \times 100 \times \frac{R}{25} = 240 \Rightarrow 15 Ω N o w R^{2} + {X_{L}}^{2} = Z^{2} \Rightarrow X_{L} = \sqrt{25^{2} - 15^{2}} = 20 Ω T h e r e f o r e L = \frac{20}{2 \times π \times 50} H = \frac{1}{5 π} H$

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