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JEE Main Physics Class 12 Alternating Currents Part 1 Questions
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Question : 80
Total: 100
Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C-R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time for needed for reducing the voltage of the fully charged series combination by half is
[2011 RS]
10 second
5 second
2.5 second
20 second
Validate
Solution:
Time constant for parallel combination = 2RC
Time constant for series combination
=
RC
2
In first case :
V
=
V
0
(
1
−
e
−
t
C
R
)
⇒
V
0
2
=
V
0
−
V
0
e
−
t
C
R
V
=
V
0
e
−
t
1
2
R
C
=
V
0
2
.......(1)
In second case :
In series grouping, equivalent capacitance
=
C
2
V
=
V
0
e
−
t
2
(
R
C
∕
2
)
=
V
0
2
.......(2)
From (1) and (2)
t
1
2
R
C
=
t
2
(
R
C
∕
2
)
⇒
t
2
=
t
1
4
=
10
4
=
2.5
sec
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