Question

In an ammeter, 5% of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be :

• A. \(\frac{G}{200}\)
• B. \(\frac{G}{199}\)
• C. 199 G
• D. 200 G
• E. None of these

Answer 1

Answer: (E)

Given: - 5% of the main current passes through the galvanometer. - The resistance of the galvanometer is \( G \).

Step 1: Calculating the Shunt Resistance \( S \)

The shunt resistance \( S \) is connected in parallel with the galvanometer such that 95% of the main current passes through the shunt. The current division formula for parallel resistances gives:

\[ \frac{I_g}{I} = \frac{S}{S + G} \]

where \( I_g \) is the current through the galvanometer and \( I \) is the total current. Given that:

\[ \frac{I_g}{I} = 0.05 \]

Substituting this value:

\[ 0.05 = \frac{S}{S + G} \]

Rearranging:

\[ 0.05(S + G) = S \] \[ 0.05G = 0.95S \] \[ S = \frac{G}{19} \]

Step 2: Calculating the Resistance of the Ammeter

The resistance of the ammeter \( R_a \) is the equivalent resistance of the galvanometer and the shunt connected in parallel:

\[ \frac{1}{R_a} = \frac{1}{G} + \frac{1}{S} \]

Substituting the value of \( S \):

\[ \frac{1}{R_a} = \frac{1}{G} + \frac{19}{G} = \frac{20}{G} \] \[ R_a = \frac{G}{20} \]

Since the resistance values provided in the options differ from this result, it is possible that additional context or conditions may influence the choice of answer.

Conclusion:

The problem seems to indicate that the correct answer is marked as a bonus question, suggesting that there may be additional considerations or assumptions needed for a precise determination.