hen a 4V battery is connected across an unknown resistor there is a current of 100 mA in the circuit.

Sure, I can help with that. The question seems to be asking for the resistance of the unknown resistor.

We can use Ohm's Law to solve this. Ohm's Law states that the voltage across a resistor is equal to the current through it times its resistance. It's usually written as V = IR.

Here's how you can solve it:

1. First, identify the given values. The voltage (V) is 4V and the current (I) is 100 mA. Note that we usually work with current in amperes, so we need to convert 100 mA to 0.1 A.

2. Next, rearrange Ohm's Law to solve for resistance (R). This gives us R = V/I.

3. Substitute the given values into the equation. This gives us R = 4V / 0.1A.

4. Solve the equation. This gives us R = 40 ohms.

So, the resistance of the unknown resistor is 40 ohms.