In an ammeter 10% of main current is passing through the galvanometer. If the resistance of the galvanometer is G, then the shunt resistance, in ohms is

Options

A. 9G
B. `G/9`
C. 90 G
D. `G/90`

Explanation

To solve the problem of finding the shunt resistance (S) in an ammeter where 10% of the main current (I) is passing through the galvanometer (Ig), we can follow these steps:

### Step 1: Understand the Current Distribution
Given that 10% of the main current is passing through the galvanometer, we can express this mathematically:
\[ I_g = 0.1 I \]

### Step 2: Determine the Current through the Shunt
Since the total current (I) is divided between the galvanometer and the shunt, the current through the shunt (I_s) can be expressed as:
\[ I_s = I - I_g \]
Substituting the value of Ig:
\[ I_s = I - 0.1 I = 0.9 I \]

### Step 3: Use Ohm's Law to Relate Voltage and Resistance
The potential difference (V) across the galvanometer and the shunt is the same because they are in parallel. According to Ohm's law, the voltage across the galvanometer can be expressed as:
\[ V = I_g \cdot G \]
And the voltage across the shunt can be expressed as:
\[ V = I_s \cdot S \]

### Step 4: Set the Voltages Equal
Since the voltages across both components are equal, we can set the equations from Step 3 equal to each other:
\[ I_g \cdot G = I_s \cdot S \]

### Step 5: Substitute Known Values
Substituting the expressions for Ig and Is:
\[ (0.1 I) \cdot G = (0.9 I) \cdot S \]

### Step 6: Solve for Shunt Resistance (S)
Now, we can solve for S:
\[ S = \frac{(0.1 I) \cdot G}{(0.9 I)} \]
The I cancels out:
\[ S = \frac{0.1 G}{0.9} \]
\[ S = \frac{G}{9} \]

### Conclusion
Thus, the shunt resistance (S) is:
\[ S = \frac{G}{9} \]