Question

A charge of $90,000coulombs$ flows through a conductor at a potential difference of $60V$ for one hour. What is the magnitude of heat energy produced?

Answer 1

Step 1: Given data and formula used

Given data:

1. Charge flowing is $Q=90,000C$
2. Potential difference is $V=60V$
3. Time for which charge flows is $t=1h=1\times 3600s=3600s$

Formula:

To find out the amount of heat energy produced, we must know the value of resistance and for that, we have to calculate the current flowing through a conductor.

The formula to calculate the current $\left(I\right)$ flowing through the conductor is

$I=\frac{Q}{t}$

Step 2: Finding the value of current

Substituting the values of charge and time into the formula to calculate the current.

$$\begin{gathered} I=\frac{90,000C}{3600s} \\ I=25A \end{gathered}$$

Step 3: Finding the value of resistance

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

$V=IR$

Where $R$ is the resistance,

Also, it can be written as $R=\frac{V}{I}$

Substituting the value of current and potential difference into the equation.

$$\begin{gathered} R=\frac{60V}{25A} \\ R=2.4\Omega \end{gathered}$$

Step 4: Calculating the amount of heat produced

According to Joule's law of heating, the amount of heat produced $\left(H\right)$ in a conductor is

$H=I^{2}Rt$

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

$$\begin{gathered} H={\left(25A\right)}^2\left(2.4\Omega \right)\left(3600s\right) \\ H=625\times 2.4\times 3600 \\ H=5400000J\left(1kJ=1000J\right) \\ H=5400kJ \end{gathered}$$

Thus, the magnitude of heat energy produced is $5400kJ$.