JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2026
- Hard
- Numerical
A moving coil of galvanometer when shunted with \(2\,\Omega\) resistance gives a full scale deflection for a current of \(500\) mA. When a resistance of \(470\,\Omega\) is connected in series it gives a full scale deflection for \(10\) V potential applied on it. The value of resistance of galvanometer coil is __________ \(\Omega\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) 50
Step-by-step Solution
Detailed explanation
Let \(G\) be the resistance of the galvanometer and \(I_g\) be the current required for full scale deflection.
When the galvanometer is shunted with \(S = 2\,\Omega\), it acts as an ammeter of range \(I = 500\text{ mA} = 0.5\text{ A}\). The potential difference across the galvanometer and the shunt is equal:
\(I_g G = (I - I_g) S\)
\(I_g G = (0.5 - I_g) \times 2\)
\(I_g G + 2 I_g = 1\)
\(I_g = \dfrac{1}{G + 2}\)
When a resistance \(R = 470\,\Omega\) is connected in series, it acts as a voltmeter of range \(V = 10\text{ V}\). The total voltage is the sum of the voltage drops:
\(V = I_g (G + R)\)
\(10 = I_g (G + 470)\)
\(I_g = \dfrac{10}{G + 470}\)
Equating the two expressions for \(I_g\):
\(\dfrac{1}{G + 2} = \dfrac{10}{G + 470}\)
\(G + 470 = 10(G + 2)\)
\(G + 470 = 10G + 20\)
\(9G = 450\)
\(G = 50\,\Omega\)
Answer: \(50\)
When the galvanometer is shunted with \(S = 2\,\Omega\), it acts as an ammeter of range \(I = 500\text{ mA} = 0.5\text{ A}\). The potential difference across the galvanometer and the shunt is equal:
\(I_g G = (I - I_g) S\)
\(I_g G = (0.5 - I_g) \times 2\)
\(I_g G + 2 I_g = 1\)
\(I_g = \dfrac{1}{G + 2}\)
When a resistance \(R = 470\,\Omega\) is connected in series, it acts as a voltmeter of range \(V = 10\text{ V}\). The total voltage is the sum of the voltage drops:
\(V = I_g (G + R)\)
\(10 = I_g (G + 470)\)
\(I_g = \dfrac{10}{G + 470}\)
Equating the two expressions for \(I_g\):
\(\dfrac{1}{G + 2} = \dfrac{10}{G + 470}\)
\(G + 470 = 10(G + 2)\)
\(G + 470 = 10G + 20\)
\(9G = 450\)
\(G = 50\,\Omega\)
Answer: \(50\)
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