Sensitivity of moving coil galvanometer is 's'. If a shunt of `((1)/(8))^(th)` of the resistance of galvanometer is connected to moving coil galvanometer, its sensitivity becomes

Options

A. `(s)/(3)`
B. `(s)/(6)`
C. `(s)/(9)`
D. `(s)/(12)`

Answer

To solve the problem, we need to understand how the sensitivity of a moving coil galvanometer changes when a shunt resistor is connected. Here is a step-by-step solution:

### Step 1: Understand the Initial Sensitivity
The sensitivity of a moving coil galvanometer is defined as the amount of current required to produce a full-scale deflection. Let’s denote the initial sensitivity as \( s \) and the current required for full-scale deflection as \( I_0 \).

### Step 2: Identify the Shunt Resistance
We are given that a shunt resistance \( R_s \) is connected, which is \( \frac{1}{8} \) of the galvanometer resistance \( R_g \). Therefore, we can express the shunt resistance as:
\[ R_s = \frac{R_g}{8} \]

### Step 3: Analyze the Circuit
When the shunt is connected in parallel with the galvanometer, the total current \( I' \) flowing through the circuit is divided between the galvanometer and the shunt. Let \( I_g \) be the current through the galvanometer and \( I_s \) be the current through the shunt. According to Kirchhoff's laws, we have:
\[ I' = I_g + I_s \]

### Step 4: Apply Ohm's Law
The voltage across the galvanometer and the shunt must be the same, so we can write:
\[ I_g \cdot R_g = I_s \cdot R_s \]
Substituting \( R_s = \frac{R_g}{8} \) into the equation gives:
\[ I_g \cdot R_g = I_s \cdot \frac{R_g}{8} \]
This simplifies to:
\[ I_g = \frac{I_s}{8} \]

### Step 5: Relate the Currents
From the previous step, we can express \( I_s \) in terms of \( I_g \):
\[ I_s = 8 I_g \]
Now substituting this back into the total current equation:
\[ I' = I_g + I_s = I_g + 8 I_g = 9 I_g \]
Thus, we have:
\[ I_g = \frac{I'}{9} \]

### Step 6: Determine the New Sensitivity
The new sensitivity \( s' \) can be defined as the current required for full-scale deflection after the shunt is connected. The new current for full-scale deflection is \( I_g \), which we found to be:
\[ I_g = \frac{I_0}{9} \]
The new sensitivity \( s' \) is inversely proportional to the current required for full-scale deflection:
\[ s' = \frac{s}{9} \]

### Conclusion
Thus, the sensitivity of the moving coil galvanometer after connecting the shunt becomes:
\[ s' = \frac{s}{9} \]