In a circuit 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G then value of the shunt is

Options

A. `19G`
B. `20G`
C. `(G)/(20)`
D. `(G)/(19)`

Answer

To find the value of the shunt resistance \( S \) when 5% of the total current passes through a galvanometer with resistance \( G \), we can follow these steps:

### Step 1: Define the total current
Let the total current in the circuit be \( I \).

### Step 2: Calculate the current through the galvanometer
Since 5% of the total current passes through the galvanometer, the current through the galvanometer \( I_G \) can be expressed as:
\[ I_G = 0.05 I \]

### Step 3: Calculate the current through the shunt
The remaining current that passes through the shunt \( I_S \) is:
\[ I_S = I - I_G = I - 0.05 I = 0.95 I \]

### Step 4: Apply the current divider rule
In a parallel circuit, the current through each branch can be calculated using the current divider rule. The current through the galvanometer is given by:
\[ I_G = \frac{S}{G + S} \cdot I \]
Substituting \( I_G = 0.05 I \) into the equation gives:
\[ 0.05 I = \frac{S}{G + S} \cdot I \]

### Step 5: Simplify the equation
We can cancel \( I \) from both sides (assuming \( I \neq 0 \)):
\[ 0.05 = \frac{S}{G + S} \]

### Step 6: Cross-multiply to solve for \( S \)
Cross-multiplying gives:
\[ 0.05 (G + S) = S \]
Expanding this results in:
\[ 0.05 G + 0.05 S = S \]

### Step 7: Rearrange the equation
Rearranging the equation to isolate \( S \):
\[ 0.05 G = S - 0.05 S \]
\[ 0.05 G = 0.95 S \]

### Step 8: Solve for \( S \)
Now, we can solve for \( S \):
\[ S = \frac{0.05 G}{0.95} = \frac{G}{19} \]

### Conclusion
Thus, the value of the shunt resistance \( S \) is:
\[ S = \frac{G}{19} \]