Consider a galvanometer shunted with 5 `Omega` resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

Options

A. 245 `Omega`
B. 344 `Omega`
C. 226 `Omega`
D. 300 `Omega`

Answer

To solve the problem of finding the resistance of the galvanometer, we can follow these steps:

### Step 1: Understand the circuit configuration
We have a galvanometer with a shunt resistor connected in parallel. The shunt resistor allows most of the current to bypass the galvanometer. Given that 2% of the total current passes through the galvanometer, we can denote the total current as \( I \).

### Step 2: Define the currents
Let:
- \( I_g \) = current through the galvanometer = \( 0.02I \) (2% of total current)
- \( I_s \) = current through the shunt resistor = \( 0.98I \) (98% of total current)

### Step 3: Use the formula for parallel resistors
For resistors in parallel, the voltage across both resistors is the same. Therefore, we can write:
\[ V_g = V_s \]
Where:
- \( V_g = I_g \cdot G \) (voltage across the galvanometer)
- \( V_s = I_s \cdot S \) (voltage across the shunt resistor)

### Step 4: Substitute the known values
We know:
- \( S = 5 \, \Omega \) (shunt resistance)
- \( I_g = 0.02I \)
- \( I_s = 0.98I \)

Thus, we can write:
\[ 0.02I \cdot G = 0.98I \cdot 5 \]

### Step 5: Simplify the equation
We can cancel \( I \) from both sides (assuming \( I \neq 0 \)):
\[ 0.02G = 0.98 \cdot 5 \]

### Step 6: Solve for \( G \)
Now, we can solve for \( G \):
\[ G = \frac{0.98 \cdot 5}{0.02} \]
Calculating the right side:
\[ G = \frac{4.9}{0.02} = 245 \, \Omega \]

### Conclusion
The resistance of the given galvanometer is \( 245 \, \Omega \).

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