Question

In the circuit shown, the $5\Omega$ resistance develops $45{\text{Js}}^{-1}$ of heat due to the flow of current through it. The current $I$ is

• A. $4\text{A}$
• B. $3\text{A}$
• C. $2\text{A}$
• D. $1\text{A}$

Answer 1

The correct option is A $4\text{A}$



Given, $\frac{H}{t}=45{\text{Js}}^{-1}$

From, the given circuit,

$V_{AB}=5I_2=15I_1$

$I_2=3I_1.......\left(1\right)$

Heat generated is,

$H=I^{2}Rt$

$\Rightarrow \frac{H}{t}=I^{2}R=\frac{V_{AB}^2}{R}$

$45=\frac{V_{AB}^2}{5}\Rightarrow V_{AB}^2=3^2\times 5^2$

$\Rightarrow V_{AB}=3\times 5=15\text{V}$

$\Rightarrow I_1=\frac{V_{AB}}{15}=\frac{15}{15}=1\text{A}$

$\Rightarrow I_2=3I_1=3\text{A}$

$\therefore I=I_1+I_2=1+3=4\text{A}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.