An ammeter reads upto 1 ampere. Its internal resistance is 0.81 ohm. To increase the range to 10 A the value of the required shunt is

Options

A. `0.03 Omega`
B. `0.3 Omega`
C. `0.9 Omega`
D. `0.09 Omega`

Explanation

To solve the problem of finding the required shunt resistance to increase the range of an ammeter from 1 A to 10 A, we can follow these steps:

### Step 1: Understand the Circuit Configuration
The ammeter (which can read up to 1 A) has an internal resistance of 0.81 ohms. To measure a current of 10 A, we need to connect a shunt resistor (S) in parallel with the ammeter. The shunt will allow most of the current to bypass the ammeter while still allowing 1 A to flow through it.

### Step 2: Define the Current Flow
Let:
- \( I \) = total current to be measured = 10 A
- \( I_G \) = current through the ammeter = 1 A
- \( I_S \) = current through the shunt = \( I - I_G = 10 A - 1 A = 9 A \)

### Step 3: Apply Kirchhoff's Voltage Law
The voltage drop across the ammeter and the shunt must be equal when they are in parallel. Therefore, we can write the equation:
\[ V = I_G \times R_G = I_S \times S \]
Where:
- \( R_G \) = internal resistance of the ammeter = 0.81 ohms
- \( S \) = resistance of the shunt

### Step 4: Substitute the Known Values
Substituting the known values into the equation gives:
\[ 1 A \times 0.81 \, \Omega = 9 A \times S \]

### Step 5: Solve for the Shunt Resistance (S)
From the equation, we can isolate \( S \):
\[ 0.81 = 9S \]
\[ S = \frac{0.81}{9} \, \Omega \]
\[ S = 0.09 \, \Omega \]

### Conclusion
The required shunt resistance to increase the range of the ammeter to 10 A is **0.09 ohms**.

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