Question

A galvanometer of resistance \(100\,\Omega\) requires \(10\,\mu\text{A}\) current for full scale deflection. Now a resistance of \(1\,\Omega\) is connected to convert it into an ammeter. The minimum current required to obtain full scale deflection is

• A. \(101\,\text{mA}\)
• B. \(1.01\,\text{mA}\)
• C. \(11.0\,\text{mA}\)
• D. \(10.1\,\text{mA}\)

Hint:

In an ammeter, most of the current flows through the low-resistance shunt, not the galvanometer.

Answer 1

The Correct Option is B

Step 1: Identify galvanometer parameters.
\[ R_g = 100\,\Omega, \quad I_g = 10\,\mu\text{A} = 10\times10^{-6}\,\text{A} \] Shunt resistance: \[ R_s = 1\,\Omega \]

Step 2: Voltage across galvanometer at full scale deflection.
\[ V = I_g R_g = 10\times10^{-6}\times100 = 10^{-3}\,\text{V} \]

Step 3: Current through shunt resistance.
\[ I_s = \frac{V}{R_s} = \frac{10^{-3}}{1} = 10^{-3}\,\text{A} = 1\,\text{mA} \]

Step 4: Total current required for full scale deflection.
\[ I = I_g + I_s = 10\,\mu\text{A} + 1\,\text{mA} = 1.01\,\text{mA} \]