JEE MAIN - Physics (2018 (Offline) - No. 4)
In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively
50, 0
50, 10
$${{1000} \over {\sqrt 2 }},10$$
$${{50} \over {\sqrt 2 }}$$
Explanation
Wattless current,
here $$\phi $$ is the angle between i and e.
Average power,
Pav = Vrms Irms cos$$\phi $$
= $${{100} \over {\sqrt 2 }} \times {{20} \over {\sqrt 2 }}$$ cos$${\pi \over 4}$$
= $${{1000} \over {\sqrt 2 }}$$ watt.
here $$\phi $$ is the angle between i and e.
Average power,
Pav = Vrms Irms cos$$\phi $$
= $${{100} \over {\sqrt 2 }} \times {{20} \over {\sqrt 2 }}$$ cos$${\pi \over 4}$$
= $${{1000} \over {\sqrt 2 }}$$ watt.
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