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JEE Main Physics Class 12 Current Electricity Part 2 Questions
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© examsnet.com
Question : 69
Total: 100
Model a torch battery of length l to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for :
[Sep. 03, 2020 (I)]
R
=
ρ
2
π
l
(
b
a
)
R
=
ρ
2
π
l
ln
(
b
a
)
R
=
ρ
π
l
ln
(
b
a
)
R
=
2
ρ
π
l
ln
(
b
a
)
Validate
Solution:
Maximum power in external resistance is generated when it is equal to internal resistance of battery i.e.,
P
R
maximum when
r
=
R
The maximum Joule heating in
R
will take place for, the resistance of small element
Δ
R
=
ρ
d
r
2
π
r
l
⇒
R
=
ρ
2
π
l
b
∫
a
d
r
r
or,
R
=
ρ
2
π
l
ln
b
a
© examsnet.com
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