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
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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
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