The resistance of an ammeter is `13 Omega` and its scale is graduated for a current upto `100 A`. After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto `750 A` by this meter. The value of shunt resistance is

Options

A. `20Omega`
B. `2Omega`
C. `0.2Omega`
D. `2kOmega`

Answer

To find the value of the shunt resistance \( R_s \) required for the ammeter, we can follow these steps:

### Step 1: Understand the Circuit Configuration
The ammeter has a resistance \( R_a = 13 \, \Omega \) and can measure a maximum current \( I_a = 100 \, A \). When a shunt resistor \( R_s \) is added, the total current \( I \) that can be measured increases to \( 750 \, A \).

### Step 2: Set Up the Current Relationships
The total current \( I \) splits between the ammeter and the shunt resistor. Thus, we can express the currents as:
- Current through the ammeter: \( I_a = 100 \, A \)
- Current through the shunt: \( I_s = I - I_a = 750 \, A - 100 \, A = 650 \, A \)

### Step 3: Apply Ohm's Law
Since the ammeter and the shunt are in parallel, the voltage across both components is the same. According to Ohm's Law, we can write:
\[ I_a \cdot R_a = I_s \cdot R_s \]
Substituting the known values:
\[ 100 \, A \cdot 13 \, \Omega = 650 \, A \cdot R_s \]

### Step 4: Solve for the Shunt Resistance \( R_s \)
Now we can rearrange the equation to solve for \( R_s \):
\[ 1300 = 650 \cdot R_s \]
\[ R_s = \frac{1300}{650} = 2 \, \Omega \]

### Conclusion
The value of the shunt resistance \( R_s \) is \( 2 \, \Omega \).

---