Question:
A galvanometer has a coil of resistance \(100\,\Omega\) showing a full scale deflection at \(50\,\mu\text{A}\). The resistance that should be added to use it as an ammeter of range \(10\,\text{mA}\) is
A galvanometer has a coil of resistance \(100\,\Omega\) showing a full scale deflection at \(50\,\mu\text{A}\). The resistance that should be added to use it as an ammeter of range \(10\,\text{mA}\) is
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To convert a galvanometer into an ammeter, connect a low resistance shunt in parallel:
\[
S=\frac{I_gG}{I-I_g}
\]
where \(G\) is galvanometer resistance and \(I_g\) is full scale current.
Updated On: Jun 26, 2026
- \(5\,\Omega\)
- \(5\times 10^{-2}\,\Omega\)
- \(0.5\,\Omega\)
- \(1\,\Omega\)
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The Correct Option is C
Solution and Explanation
Step 1: Identify the galvanometer data.
Resistance of galvanometer: \[ G=100\,\Omega \] Full scale deflection current: \[ I_g=50\,\mu\text{A} \] \[ I_g=50\times 10^{-6}\,\text{A} \] Desired ammeter range: \[ I=10\,\text{mA} \] \[ I=10\times 10^{-3}\,\text{A} \]
Step 2: Use the shunt resistance formula.
To convert a galvanometer into an ammeter, a small resistance \(S\) is connected in parallel.
The formula is \[ S=\frac{I_gG}{I-I_g} \]
Step 3: Substitute the values.
\[ S=\frac{(50\times 10^{-6})(100)} {10\times 10^{-3}-50\times 10^{-6}} \] \[ S=\frac{5\times 10^{-3}} {9.95\times 10^{-3}} \] \[ S\approx 0.5\,\Omega \]
Step 4: Final conclusion.
Hence, the required resistance is \[ \boxed{0.5\,\Omega} \]
Resistance of galvanometer: \[ G=100\,\Omega \] Full scale deflection current: \[ I_g=50\,\mu\text{A} \] \[ I_g=50\times 10^{-6}\,\text{A} \] Desired ammeter range: \[ I=10\,\text{mA} \] \[ I=10\times 10^{-3}\,\text{A} \]
Step 2: Use the shunt resistance formula.
To convert a galvanometer into an ammeter, a small resistance \(S\) is connected in parallel.
The formula is \[ S=\frac{I_gG}{I-I_g} \]
Step 3: Substitute the values.
\[ S=\frac{(50\times 10^{-6})(100)} {10\times 10^{-3}-50\times 10^{-6}} \] \[ S=\frac{5\times 10^{-3}} {9.95\times 10^{-3}} \] \[ S\approx 0.5\,\Omega \]
Step 4: Final conclusion.
Hence, the required resistance is \[ \boxed{0.5\,\Omega} \]
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