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17/07/2021 3:53 pm
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How does the resistance of a wire change when :
(i) its length is tripled?
(ii) its diameter is tripled?
(iii) its material is changed to one whose resistivity is three times?
1 Answer
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17/07/2021 4:01 pm
R = \(\rho \frac{I}{A}\)
(i) I = 3I
R' = \(\rho \frac{3I}{A}\)
= 3R
Resistance gets tripled.
(ii) d = 3d
R = \(\rho \frac{I}{A}\)
= R = \(\rho \frac{I}{\pi r^2}\)
= \(\rho \frac{I}{\pi (\frac{d}{2})^2}\)
R' = \(\rho \frac{I}{\pi (\frac{3d}{2})^2}\)
= R' = \(\frac{1}{9} \rho\)\( \frac{I}{\pi (\frac{d}{2})^2}\)
= \( \frac{R}{9}\)
Resistance becomes \( \frac{1}{9}th\)
(iii) R = \(\rho \frac{I}{A}\)
ρ = 3ρ
R' = 3ρ\(\frac{I}{A}\) = 3R
Resistance becomes 3 times