JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2016
- Hard
- MCQ
A \(50\,\Omega \) resistance is connected to a battery of \(5\,V\). A galvanometer of resistance \(100\, \Omega \) is to be used as an ammeter to measure current through the resistance, for this a resistance \(r_s\) is connected to the galvanometer. Which of the following connections should be employed if the measured current is within \(1\% \) of the current without the ammeter in the circuit ?
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(r_s = 0.5\, \Omega \) in parallel with the galvanometer
Step-by-step Solution
Detailed explanation
As we know, \(\mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{5}{50}=0.1\)
\(I' = 0.099\)
When Galvanometer is connected
\(R_{e q}=50+\frac{100 S}{100+S}=\frac{V}{I}\)
\(\Rightarrow \frac{100 \mathrm{S}}{100+\mathrm{S}}=\frac{5}{0.099}-50\)
\(\Rightarrow \frac{100 \mathrm{S}}{100+\mathrm{S}}=50.50-50 \Rightarrow \frac{100 \mathrm{S}}{100+\mathrm{S}}=0.5\)
\(\Rightarrow 100 \mathrm{S}=50+0.55 \Rightarrow 99.5 \mathrm{S}=50\)
\(S=\frac{50}{99.05}=0.5 \,\Omega\)
So, shunt of resistance \(=0.5\, \Omega\) is onnected in parallel with the galvanometer.
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