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JEE Main Physics Class 12 Alternating Currents Part 1 Questions
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© examsnet.com
Question : 63
Total: 100
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to
Q
0
and then connected to the L and R as shown below :
If a student plots graphs of the square of maximum charge
(
Q
Max
2
)
on the capacitor with time(t) for two different values
L
1
and
L
2
(
L
1
>
L
2
)
of
L
then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)
[2015]
Validate
Solution:
From KVL at any time t
q
c
−
i
R
−
L
d
i
d
t
=
0
i
=
−
d
q
d
t
⇒
q
c
+
d
q
d
t
R
+
L
d
2
q
d
t
2
=
0
d
2
q
d
t
2
+
R
L
d
q
d
t
+
q
L
c
=
0
From damped harmonic oscillator, the amplitude is given
by
A
=
A
o
e
−
d
t
2
m
Double differential equation
d
2
x
d
t
2
+
b
m
d
x
d
t
+
k
m
x
=
0
Q
max
=
Q
o
e
−
R
t
2
L
⇒
Q
max
2
=
Q
o
2
e
−
R
t
L
Hence damping will be faster for lesser self inductance.
© examsnet.com
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