The specific resistance p (rho) of a circular wire of radius r, resistance R & length L is given by p = π^2R/ l. Given r=(0.24+-0.02) cm, R = (30+-1) ohm, l = (4.80+-0.01) cm. The percentage error in specific resistance is nearly
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The specific resistance is given as :
ρ=
l
πr
2
R
Differentiating both sides given (in terms of relative error ):-
ρ
ΔP
=2
r
Δr
+
R
ΔR
+
l
Δl
→(2)
From given data,
r=0.24±0.02cm⇒
r
Δr
=
0.24
0.02
=
12
1
R=30±1Ω⇒
R
ΔR
=
30
1
l=4.80±0.01cm⇒
L
ΔL
=
4.80
0.07
=
480
1
Hence from (1),
ρ
ΔP
=2×
12
1
+
30
1
+
480
1
=20.2%
Explanation:
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