An ammeter of resistance 1.5 `Omega` can measure currents upto 1 A. The value of shunt resistance to measure current upto 4 A is

Options

A. `0.5 Omega`
B. `1 Omega`
C. `1.5 Omega`
D. `0.2 Omega `

Explanation

To find the value of the shunt resistance (Rs) required to measure a current of up to 4 A using an ammeter with a resistance (Rg) of 1.5 Ω that can measure up to 1 A, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
The ammeter is connected in parallel with the shunt resistor. The total current (I) flowing through the circuit splits between the ammeter (Ig) and the shunt resistor (Is).

2. **Current Values**:
- The maximum current that the ammeter can measure (Ig) = 1 A.
- The total current we want to measure (I) = 4 A.
- Therefore, the current through the shunt resistor (Is) = I - Ig = 4 A - 1 A = 3 A.

3. **Using Ohm's Law**:
The voltage across the ammeter (Rg) and the shunt resistor (Rs) is the same since they are in parallel. According to Ohm's Law:
\[ V = I \times R \]
For the ammeter:
\[ V = Ig \times Rg = 1 A \times 1.5 \, \Omega = 1.5 \, V \]

4. **Voltage Across the Shunt Resistor**:
The voltage across the shunt resistor (Rs) can also be expressed as:
\[ V = Is \times Rs = 3 A \times Rs \]

5. **Setting the Voltages Equal**:
Since the voltages across both resistors are equal:
\[ 1.5 \, V = 3 A \times Rs \]

6. **Solving for Rs**:
Rearranging the equation to find Rs:
\[ Rs = \frac{1.5 \, V}{3 A} = 0.5 \, \Omega \]

### Final Answer:
The value of the shunt resistance (Rs) required to measure a current of up to 4 A is **0.5 Ω**.

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