BITSAT 2023Paper 2
- Exam
- BITSAT
- Year
- 2023
- Paper
- Paper 2
- Subject
- Physics
- Chapter
- Mathematics in Physics
BITSAT 2023 · Paper 2 · Physics · Mathematics in Physics
Two resistances are given as R_1=(10 ±0.5) and R_2=(15 ± 0.5) . The...
Two resistances are given as and . The percentage error in the measurement of equivalent resistance when they are connected in parallel is
Options
- A
6.33 - B
2.33 - C
4.33 - D
5.33
Correct answer
C.
4.33
Step-by-step solution
Equivalent resistance in parallel combination is given byDifferentiating both sides, we get\begin{aligned} & \frac{\Delta R_{\text{eq }}}{\mathrm{R}_{\mathrm{eq}^2}=\frac{\Delta \mathrm{R}_1}{\mathrm{R}_1^2}+\frac{\Delta \mathrm{R}_2}{\mathrm{R}_2^2} \\ & \Rightarrow \frac{\Delta \mathrm{R}_{\mathrm{eq}}}{\mathrm{R}_{\mathrm{eq}}}=\left(\frac{\Delta \mathrm{R}_1}{\mathrm{R}_1^2}+\frac{\Delta \mathrm{R}_2}{\mathrm{R}_2^2}\right) \mathrm{R}_{\mathrm{eq}} \\ & =\left(\frac{0.5}{100}+\frac{0.5}{225}\right) \cdot 6=\left(\frac{6 \times 0.5}{25}\right)\left(\frac{1}{4}+\frac{1}{9}\right)=\frac{13}{300} \\ & \frac{\Delta \mathrm{R}_{\mathrm{eq}}}{\mathrm{R}_{\mathrm{eq}}} \times 100=\frac{13}{3}=4.33 \%\end{aligned}