Step 1: Understanding the Concept:
A galvanometer is converted into an ammeter by connecting a low resistance, called a shunt, in parallel with it.
Because they are in parallel, the potential difference across the galvanometer and the shunt must be equal.
Step 2: Key Formula or Approach:
The potential difference equality gives: \( I_g \times G = I_s \times S \), where:
\( I_g \) is the current through the galvanometer.
\( G \) is the resistance of the galvanometer.
\( I_s \) is the current through the shunt.
\( S \) is the resistance of the shunt.
Total current \( I = I_g + I_s \).
Step 3: Detailed Explanation:
Let the total current be \( I \).
It is given that only \( 5% \) of the total current passes through the galvanometer.
Therefore, the galvanometer current is \( I_g = 5% \text{ of } I = \frac{5}{100} \times I = \frac{I}{20} \).
The remaining current must pass through the shunt.
The shunt current is \( I_s = I - I_g = I - \frac{I}{20} = \frac{19I}{20} \).
Now apply the parallel potential difference condition:
\[ I_g \times G = I_s \times S \]
Substitute the expressions for \( I_g \) and \( I_s \):
\[ \left( \frac{I}{20} \right) \times G = \left( \frac{19I}{20} \right) \times S \]
Cancel the common terms \( I \) and \( 20 \) from both sides:
\[ 1 \times G = 19 \times S \]
Rearrange to find the shunt resistance \( S \):
\[ S = \frac{G}{19} \]
Step 4: Final Answer:
The resistance of the shunt must be \( \frac{G}{19} \).