Question

The value of the resistance $R$ in the circuit shown so that electric bulb consumes the rated power is:

• A. $4$ ohm
• B. $6$ ohm
• C. $8$ ohm
• D. $10$ ohm

Answer 1

The correct option is B $6$ ohm

The diagram shows that if voltage of 3V is applied to the bulb, it consumes 0.5W of power.

Its resistance can be calculated as follows

$P=\frac{V^2}{R_b}$ $\therefore R_b=\frac{V^2}{P}=18\Omega$

Total current passing through the entire circuit is

$I=\frac{6}{0.5+4+R_p}$

Voltage across bulb is same as that across the parallel combination

$3=\frac{6R_p}{0.5+4+R_p}$

$6R_p=(3\times 4.5)+3R_p$

$\therefore R_p=4.5\Omega$

We know that $R_p=\frac{R\times R_b}{R+R_b}$

$\therefore \frac{45}{10}=\frac{18R}{18+R}$

$\therefore \frac{9}{2}=\frac{18R}{18+R}$

$\therefore \frac{1}{2}=\frac{2R}{18+R}$

$18+R=4R$ $\therefore R=6\Omega$