Question

In L-C-R series circuit, an alternating emf (e) and current
(i) are given by the equations
e = 100 sin (100t) volt,
and
i = 100 sin (100t+pi/3) mA
The average power dissipated in the circuit will be
a. 100 W
b. 10 W
c. 5 W
d. 2.5 W​

Answer 1

Answer:

ANSWER

Comparing the given e.m.f equation with e=e

o

sinwt

We get peak value of e.m.f e

o

=100 volt

Thus r.m.s value of e.m.f e

rms

=

2

e

o

=

2

100

Similarly, on comparing the given current equation with i=i

o

sin(wt+ϕ)

We get peak value of current i

o

=100 mA

Thus r.m.s value of current i

rms

=

2

i

o

=

2

100

mA

Also we get ϕ=

3

π

Thus average power dissipated <P>=e

rms

i

rms

cosϕ

∴ <P>=

2

100

.

2

100

×10

−3

.

2

1

⟹ <P>=2.5W