Current Electricity 1 Question 25
25. A copper wire is stretched to make it $0.1 %$ longer. What is the percentage change in its resistance?
(1978)
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Answer:
Correct Answer: 25. $0.2 %$ increase
Solution:
- $R=\rho \frac{l}{A}=\frac{\rho \cdot l}{V / l}=\frac{\rho l^{2}}{V} \quad(V=$ volume of wire $)$
$$ \left.\therefore \quad R \propto l^{2} \quad \text { ( } \rho \text { and } V=\text { constant }\right) $$
For small percentage change
$%$ change $R=2(%$ change in $l)=2(0.1 %)=0.2 %$
Since $R \propto l^{2}$, with increase in the value of $l$, resistance will also increase.
