In the circuit shown below, current iis supplied by battery when both switches S1 and S2 are open. As we close the switches S1 and S2, the current supplied by battery becomes 602 692 692 w S2 S, S um w 692 692 692 24 V
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Δi=(i
2
−i
1
)=
R
V
[1−e
−(
2L
R
)t
]
−
R
V
[1−e
(
L
R
)t
]
R
V
[e
−(
L
R
)t
−e
−(
2L
R
)t
]
For (Δi)
max
dt
d(Δi)
=0
R
V
[−
L
R
e
−(
L
R
)t
−(−
2L
R
)e
−(
2L
R
)t
]=0
e
−(
L
R
)t
=
2
1
e
−(
2L
R
)t
e
−(
2L
R
)t
=
2
1
(
2L
R
)t=ℓn2
t=
R
2L
ℓn2→ time when i is maximum.
i
max
=
R
V
[e
L
R
(
R
2L
ℓn2)
−e
−(
2L
R
)(
R
2L
ℓn2)
]
∣I
max
∣=
R
V
∣
∣
∣
∣
∣
[
4
1
−
2
1
]
∣
∣
∣
∣
∣
=
4
1
R
V
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