**Calculating the Potential Difference across the Resistor**

To calculate the potential difference across a resistor, we can use Ohm's law. Ohm's law states that the potential difference across a resistor is equal to the current passing through it multiplied by its resistance. The formula for Ohm's law is:

V = I * R

Where:
- V is the potential difference (in volts)
- I is the current (in amperes)
- R is the resistance (in ohms)

In this case, we are given that 100J of heat is produced each second in a 4-ohm resistance. Heat is a form of energy, and in electrical circuits, it is generated by the flow of current through a resistor.

**Step 1: Calculating the Current**

Since we are given the amount of heat produced per second, we can assume that this heat is generated by the electrical energy dissipated in the resistor. The unit of heat is joules (J), and power is the rate at which heat is produced or consumed. Therefore, we can use the following formula to calculate the current:

Power = Current * Potential Difference

Since 100J of heat is produced each second, the power is 100W (Watt), as power is equal to energy divided by time. Given that the resistance is 4 ohms, we can rearrange the formula to solve for the current:

100W = I * V

I = 100W / V

**Step 2: Calculating the Potential Difference**

Now, let's substitute the value of the resistance (4 ohms) into Ohm's law to solve for the potential difference:

V = I * R

V = (100W / V) * 4Ω

Multiplying both sides of the equation by V:

V^2 = 100W * 4Ω

V^2 = 400WΩ

Taking the square root of both sides:

V = √(400WΩ)

V ≈ 20V

Therefore, the potential difference across the 4-ohm resistor is approximately 20 volts.