Question

A current of 5 A flows through a 120 $\Omega $ resistor. What is the rate at which heat energy is produced in the resistor?

Answer 1

Hint: Firstly, we have to find what expressions are given in the question. After that, with the help of the given expression. We have to calculate the rate at which heat energy is produced with the help of the \[I{}^\text{2}Rt\] expression.

Formula used:
Here, the formula used is \[I{}^\text{2}Rt\]
Where $I$ is the current flowing through that resistor, $R$ is the resistance of that resistor, and $t$ is the time in which heat energy is produced or generated.

Complete step by step solution:
It is given in the question that,
$I=5A$
$R=120\Omega $
So, the total amount of heat energy generated due to a given resistor,
Heat Energy Produced /Consumed, H\[=I{}^\text{2}Rt\]
Therefore, the rate at which heat energy is produced/Consumed
\[=\dfrac{I{}^\text{2}Rt}{t}\]
\[=I{}^\text{2}R\]
$={{5}^{2}}\times 120$
$=25\times 120$
\[=3000{J}/{s}\;\]
\[=3000\]W
Hence, the rate at which heat energy is dissipated or you can say as produced in the resistor in the circuit is \[3000\]W.

Additional Information:
heat denoted by the symbol 'H' is defined as the energy transferred from one body to another as the result of a difference in their temperature. Let's say that two bodies at different temperatures are brought together. Then, energy is being transferred or we can simply say that heat flows from the hotter body to the colder body. The effect of this transfer of energy usually, but not always. It only happens due to an increase in the temperature of the colder body and a decrease in the temperature of the hotter body. Also, the unit of Heat is either joule per second (‘${J}/{s}\;$’) or watt ('W').

Note: Don't forget to divide the expression of heat energy produced by time. As without doing that we will be unable to get the desired result in form of a rate and also, remember to put the either watt ('W') or joule per second (‘${J}/{s}\;$’) symbol in the result.