The ratio of the lengths of two wires is 2 : 1 and the ratio of their radii is 1 : 2. Calculate the ratio of the resistance of the two wires if their resistivity is in a 3 : 4 ratio.
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R
1
=(
ρ
2
ρ
1
)(
L
2
L
1
)(
A
1
A
2
)
=(
ρ
2
ρ
1
)(
L
2
L
1
)(
r
1
2
r
2
2
)
=
3
2
×
5
3
×(
7
2
)
−2
[
r
1
r
2
=
2
7
]
=
5
2
×(
49
4
)
−2
=
5
2
×
4
49
R
2
R
1
=
10
49
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