Question

A resistor develops 1600 J of thermal energy in 50 s when a current of 2 A flows through it. If the current is increased to 10 A, what will be the thermal energy developed in the same amount of time?

• A. 40 KJ
• B. 16 KJ
• C. 80 KJ
• D. 64 KJ

Answer 1

The correct option is A 40 KJ

Well, this is a direct application of the formula. Now you could ask, how we can find the value of resistance and time of heat. Well the answer is that we don’t have to.
In the first case, a 2A current causes 1600J of thermal energy in a resistor.
In the second case, 10A of the current through the same resistor for the same time cause some amount of heat which we have to find. Since R and t are the same we can treat them as constants.
Meaning , $H\propto i^2$
And any proportionality can be made a ratio.
$\frac{H_1}{H_2}=\frac{i_1^2}{i_2^2}$
Since $\frac{i_1}{i_2}is\frac{2}{10},$
$\frac{H_1}{H_2}={\left(\frac{2}{10}\right)}^2$
$H_2=1600\times 25=40KJ$