Question 228: AC fundamentals

Question

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

Accepted Answer

Wattless current,
here  $$\phi $$  is the angle between i and e.
Average power,
P
av
= V
rms
I
rms
cos$$\phi $$
= $${{100} \over {\sqrt 2 }} 	imes {{20} \over {\sqrt 2 }}$$ cos$${\pi  \over 4}$$
= $${{1000} \over {\sqrt 2 }}$$ watt.

Answer

50, 0

Answer

50, 10

Answer

$${{1000} \over {\sqrt 2 }},10$$

Answer

$${{50} \over {\sqrt 2 }}$$

AC fundamentals

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

Choose the correct answer: