Question

400 joules of heat is produced per second in a $4\Omega$ resistor. What is the potential difference across the resistor?

Answer 1

Step 1: Given data and formula

Given data:

The heat produced is $H=400J$

Resistance is $R=4\Omega$

The time in which heat is produced is $t=1s$

Formula:

According to Joule's law of heating, the amount of heat produced in a conductor is

$H=I^{2}Rt$

where $I$ is the current flowing through the conductor.

Also, it can be written as

$I=\sqrt{\frac{H}{Rt}}$

Step 2: Finding the current

Substituting the values of heat produced, resistance and time into the equation to calculate the current.

$$\begin{gathered} I=\sqrt{\frac{400J}{4\Omega \times 1s}} \\ I=\sqrt{\frac{400}{4}} \\ I=10A \end{gathered}$$

Step 3: Finding the potential difference across the resistor

According to Ohm's law, the relationship between potential difference and current is

$V=IR$

where $V$ is the potential difference.

Substituting the values of current and resistance into the equation to calculate the potential difference.

$$\begin{gathered} V=10A\times 4\Omega \\ V=40V \end{gathered}$$

Final answer: Thus, the potential difference across the resistor is $40V$.