A 50 Ω resistance is connected to a battery of 5 V. A galvanometer of… | JEE Main 2016 (9 Apr, Shift 1)

Q178JEE Main 2016 · 9 APR · SHIFT 1Medium

Kirchhoff's Laws & Measuring Instruments

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 rs 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?

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Answer: (a)

True current $I = \frac{5}{50} = 0.1\text{ A}$ . To stay within 1%, $\frac{50}{50 + R_A} \ge 0.99 \Rightarrow R_A \le 0.505\ \Omega$ .
An ammeter needs a small shunt in parallel with the galvanometer.
With $r_s = 0.5\ \Omega$ in parallel: $R_A = \frac{100 \times 0.5}{100.5} \approx 0.497\ \Omega$ , which works.
So the answer is (a) $r_s = 0.5\ \Omega$ in parallel.

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