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)

None of these

Answer 2

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.