Mathematics in Physics

JEE Main level, single correct, medium

117 of 121

Question 117 of 121

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3%3 \% each, then error in the value of resistance of the wire is

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Answer: (A) 6%6 \%

R=Vi\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}
⇒∣ΔRR∣=∣ΔVV∣+∣Δii∣\Rightarrow \quad\left|\frac{\Delta \mathrm{R}}{\mathrm{R}}\right|=\left|\frac{\Delta \mathrm{V}}{\mathrm{V}}\right|+\left|\frac{\Delta \mathrm{i}}{\mathrm{i}}\right|
ΔVV×100=3\frac{\Delta \mathrm{V}}{\mathrm{V}} \times 100=3
⇒ΔVV=0.03\Rightarrow \quad \frac{\Delta \mathrm{V}}{\mathrm{V}}=0.03
Similarly, Δii=0.03\frac{\Delta i}{i}=0.03
Hence ΔRR=0.06\frac{\Delta \mathrm{R}}{\mathrm{R}}=0.06
So percentage error is ΔRR×100=6%\frac{\Delta \mathrm{R}}{\mathrm{R}} \times 100=6 \%

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