When a 4V battery is connected across an unknown resistor there is a current of 100 mA in the circuit. The value of the resistance of the resistor is:

Options

A. `4 omega`
B. `40 omega`
C. `400 omega`
D. `0.4 omega`

Explanation

To find the value of the resistance of the unknown resistor when a 4V battery is connected across it and a current of 100 mA flows through the circuit, we can use Ohm's Law. Ohm's Law states that:

\[ V = I \times R \]

Where:
- \( V \) is the voltage (in volts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).

### Step-by-Step Solution:

1. **Identify the given values**:
- Voltage \( V = 4 \) volts
- Current \( I = 100 \) mA

2. **Convert current from milliampere to ampere**:
- \( 100 \) mA = \( 100 \times 10^{-3} \) A = \( 0.1 \) A

3. **Use Ohm's Law to find resistance**:
- Rearranging Ohm's Law gives us:
\[ R = \frac{V}{I} \]

4. **Substitute the known values into the equation**:
- \( R = \frac{4 \text{ V}}{0.1 \text{ A}} \)

5. **Calculate the resistance**:
- \( R = \frac{4}{0.1} = 40 \) ohms

6. **Conclusion**:
- The value of the resistance of the unknown resistor is **40 ohms**.