a series LCR circuit with L=0.12H , C=4.8×10-7F, R =23ohm connected to a variable frequencysupply . At what frequency is the current maximum
Answers
Answer:
Explanation:
a)
V
o
=
2
V=325.2 volts
Tt resonance, ω
R
L=1/(ω
R
C)
We know that,
⇒ω
R
=1/
LC
=4166.67rad/s
Resonant frequency,
ν
R
=ω
R
/2π
=663.48Hz
I
o
=V
o
/R=14.14A
(b)
Maximum power absorbed
P=
2
1
I
o
2
R
2
1
(14.14)
2
×23
⇒2299.3W
(c)
The angular frequencies at which the power would be half of the power at resonant frequency will be:
ω
′
=ω
R
±Δω
Here, Δω=
2L
R
⇒Δω=
2×0.12
23
⟹95.83 rad/s
So,
ω
1
′
=4166.67+95.83
=4262.3 rad/s
ω
2
′
=4166.67−95.83
=4070.87 rad/s
The amplitude of current at these frequencies will be the RMS value.
I=
2
I
0
⇒
1.414
14.14
⇒10 A
(d)
Q factor is given by
Q=
R
1
C
L
=
23
1
480×10
−9
0.12
=21.74