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Exam
JEE Main
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Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

A current carrying conductor obeys Ohm's law (V=R I) . If the...

A current carrying conductor obeys Ohm's law (V=RI)(V=R I). If the current passing through the conductor is I=(5±0.2)I=(5 \pm 0.2) A and voltage developed is V=(60±6)VV=(60 \pm 6) \mathrm{V}, then find the percentage of error is resistance, RR

Options

  1. A18
  2. B6
  3. C14
  4. D2

Correct answer

C. 14

Step-by-step solution

Given, current passing through the conductor, I=(5 ±\pm0.2) A,Δ\mathrm{A}, \DeltaI=0.2  A\mathrm{~A}Voltage developed, V=(60±6)V⇒\DeltaV=6 V\begin{array}{rlrl}& & V & =(60 \pm6) \mathrm{V}\\ \Rightarrow \quad & \DeltaV & =6 \mathrm{~V} \end{array}By Ohm's law, V=RIR=VIΔRR=ΔVV+ΔII=660+0.25=0.1+0.04ΔRR=0.14∴ΔRR×100=0.14×100=14%\begin{aligned}V & =R I \\ R & =\frac{V}{I}\\ \frac{\Delta R}{R}& =\frac{\Delta V}{V}+\frac{\Delta I}{I}\\ & =\frac{6}{60}+\frac{0.2}{5}\\ & =0.1+0.04 \\ \frac{\Delta R}{R}& =0.14 \\ \therefore \quad \frac{\Delta R}{R} \times100 & =0.14 \times100=14 \% \end{aligned}
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