Question

A resistor develops $500\text{J}$ of thermal energy in $20\text{s}$ when a current of $1.5\text{A}$ is passed through it. If the current is increased from $1.5\text{A}$ to $3\text{A}$, what will be the energy developed in $20\text{s}$.

• A. $500\text{J}$
• B. $1000\text{J}$
• C. $2000\text{J}$
• D. $1500\text{J}$

Answer 1

The correct option is C $2000\text{J}$

Thermal energy developed is given as: $$H=I^{2}Rt$$ Time and resistor both are same, only current is changed.

$\Rightarrow \frac{H_1}{H_2}={\left(\frac{I_1}{I_2}\right)}^2$

$\Rightarrow \frac{500}{H_2}={\left(\frac{1.5}{3}\right)}^2$

$\therefore H_2=500\times {\left(\frac{3}{1.5}\right)}^2=2000\text{J}$