Question

What will be the frequency of the instantaneous power of a purely inductive system if that of the source is 'f'? Explain.

Answer 1

for  an AC source we will take the voltage as

$V = V_o sin(2\pi f t)$

its frequency is "f"

now it is connected across pure inductor

then current in the inductor is 90 degree behind in phase

so current is given as

$i = i_o sin(2 \pi f t - \frac{\pi}{2})$

now for instantaneous power

$P = i V$

$P = i_o sin(2 \pi f t - \frac{\pi}{2})*  V_o sin(2\pi f t)$

$P = i_o V_o sin(2\pi f t) cos(2 \pi f t)$

$P = \frac{i_o V_o}{2} sin(4 \pi f t)$

so the frequency of instantaneous power is double then the frequency of voltage source.