Question

The resistance of the galvanometer and shunt of an ammeter are 90 ohms and 10 ohms respectively, then the fraction of the main current passing through the galvanometer and the shunt respectively are:

• A. \( \frac{1}{90} \) and \( \frac{1}{10} \)
• B. \( \frac{1}{10} \) and \( \frac{1}{90} \)
• C. \( \frac{9}{10} \) and \( \frac{1}{10} \)
• D. \( \frac{1}{90} \) and \( \frac{9}{10} \)

Hint:

In ammeters, the current is divided between the galvanometer and the shunt. The fraction of current through the galvanometer is inversely proportional to its resistance.

Answer 1

The Correct Option is C

The total current is divided into two parts, one flowing through the galvanometer and the other through the shunt. The fraction of the current passing through the galvanometer is given by the ratio of the resistance of the galvanometer to the total resistance (which is the sum of the resistances of the galvanometer and the shunt): \[ I_{\text{galv}} = \frac{R_{\text{galv}}}{R_{\text{galv}} + R_{\text{shunt}}} \] Substituting the given values: \[ I_{\text{galv}} = \frac{90}{90 + 10} = \frac{90}{100} = \frac{9}{10}. \] The remaining fraction of the current flows through the shunt: \[I_{\text{shunt}} = 1 - I_{\text{galv}} = 1 - \frac{9}{10} = \frac{1}{10}. \] Thus, the fraction of the current passing through the galvanometer is \( \frac{9}{10} \) and the fraction passing through the shunt is \( \frac{1}{10} \).