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Alternating Current
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Section:
Physics
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© examsnet.com
Question : 3
Total: 13
A series LCR circuit is connected to a
45
s
i
n
‌
(
ω
t
)
Volt source. The resonant angular frequency of the circuit is
10
5
‌
rad
‌
s
−
1
and current amplitude at resonance is
I
0
. When the angular frequency of the source is
ω
=
8
×
10
4
rad s
‌
−
1
, the current amplitude in the circuit is
0.05
I
0
. If
L
=
50
‌
mH
, match each entry in List-I with an appropriate value from List-II and choose the correct option.
List-I
List-II
(P)
I
0
in
mA
(1) 44.4
(Q) The quality factor of the circuit
(2) 18
(R) The bandwidth of the circuit in rad s
(3) 400
(S) The peak power dissipated at resonance in Watt
(4) 2250
(5) 500
[JEE Adv 2023 P1]
P
→
2
,
Q
→
3
,
R
→
5
,
S
→
1
P
→
3
,
Q
→
1
,
R
→
4
,
S
→
2
P
→
4
,
Q
→
5
,
R
→
3
,
S
→
1
P
→
4
,
Q
→
2
,
R
→
1
,
S
→
5
Validate
Solution:
As per the given information :
‌
1
√
L
C
=
10
5
...(i)
I
0
=
‌
45
R
...(ii)
0.05
I
0
=
‌
45
√
R
2
+
(
0.8
X
L
0
−
‌
5
4
X
C
0
)
2
Where
X
L
0
=
X
C
0
are at resonant frequencies
On solving,
R
≃
‌
450
Ω
4
⇒
I
0
≃
400
‌
mA
Quality factor
Q
=
‌
1
R
√
‌
L
C
≃
44.44
Q
=
‌
ω
0
∆
ω
⇒
∆
ω
≃
2250
‌
rad
‌
/
‌
s
Peak power
=
45
×
‌
400
1000
W
⇒
Correct match is option (B)
© examsnet.com
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