JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2018
- Hard
- Numerical
In a circuit for finding the resistance of a galvanometer by half deflection method, a \(6\,V\) battery and a high resistance of \(11\,k\Omega \) are used. The figure of merit of the galvanometer \(60\,\mu A/\) division. In the absence of shunt resistance, the galvanometer produces a deflection of \(\theta = 9\) divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\) is closest to .................. \(\Omega\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(110\)
Step-by-step Solution
Detailed explanation
Figure of merit of a galvanometer is the current required to produce a deflection of one division in the galvancmeter i.e., figure of merit \(=\frac{\mathrm{I}}{\theta}\)
\(\mathrm{I}=\frac{\varepsilon}{\mathrm{R}+\mathrm{G}} \quad \mathrm{G}=\frac{1}{9}\, \mathrm{K}\, \Omega\)
\(\frac{1}{2}=\frac{\varepsilon}{R+\frac{G S}{G+\bar{S}}} \times \frac{S}{S+G} \Rightarrow \frac{1}{2}=\frac{\varepsilon S}{R(S+G)+G S}\)
\(S=\frac{R G \times \frac{1}{2}}{\varepsilon-\frac{(R+G) I}{2}}\)
\(S=\frac{11 \times 10^{3} \times \frac{1}{2} \times 10^{2} \times 270 \times 10^{-6}}{6-\left(\frac{6}{2}\right)}=110\, \Omega\)
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