Question

The circuit given below is for the operation of an industrial fan. The resistance of the fan is $3ohm$. The regulator provided with the fan is a fixed resistor and a variable resistor in parallel. Under what value of the variable resistance given, power transferred to the fans will be maximum? The power source of the fan is a dc source with internal resistance of $6ohm$

• A. 3 $\Omega$
• B. $0$
• C. $\infty$
• D. $6$$\Omega$

Answer 1

The correct option is B $0$

The power transferred to fan is given as $P=V^2/R$, where $R$ is the total resistance of the circuit. As power is inversely proportional to total resistance. So for maximum power, the total resistance should be minimum. Total resistance here is $R=\frac{6r}{6+r}+3$. $r$ is the variable resistance.

$R$ is minimum when $r=0$.