CUET · PHYSICS · PYQ PAPER 2024
A metallic wire of uniform area of cross section has a resistance R, resistivity \(\rho\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity and power rating at V volts are now denoted by R', and P' respectively. The corresponding values are correctly related as __________ . Fill in the blank with the correct answer from the options given below
- A \(\rho' = 2\rho, R' = 2R, P' = 2P\)
- B \(\rho' = 1/2\rho, R' = 1/2R, P' = 1/2P\)
- C \(\rho' = \rho, R' = 16R, P' = 1/16P\)
- D \(\rho' = \rho, R' = 1/16R, P' = 16P\)
Answer & Solution
Correct Answer
(C) \(\rho' = \rho, R' = 16R, P' = 1/16P\)
Step-by-step Solution
Detailed explanation
\(\rho' = \rho\) \(A' = \pi (r/2)^2 = A/4\) \(L' = (AL)/A' = (AL)/(A/4) = 4L\) \(R' = \rho' \frac{L'}{A'} = \rho \frac{4L}{A/4} = 16 \rho \frac{L}{A} = 16R\) \(P' = \frac{V^2}{R'} = \frac{V^2}{16R} = \frac{1}{16}P\) \(\rho' = \rho, R' = 16R, P' = 1/16P\)
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