Question

Two different light bulbs are in a DC circuit attached with a $18V$ battery . The two bulbs are rated at $4.5$ watts $\left(B_1\right)$ and $6.75$ watts $\left(B_2\right)$ each. Find out the resistances of the two light bulbs $\left(B_1\right)$ and $\left(B_2\right)$?

• A. $B_1$ is $48\Omega$, and $B_2$ is $72\Omega$
• B. $B_1$ is $72\Omega$, and $B_2$ is $48\Omega$
• C. $B_1$ is $2.67\Omega$, and $B_2$ is $4\Omega$
• D. $B_1$ is $4\Omega$, and $B_2$ is $2.67\Omega$
• E. $B_1$ is $20.25\Omega$, and $B_2$ is $45.56\Omega$

Answer 1

The correct option is B $B_1$ is $72\Omega$, and $B_2$ is $48\Omega$

Power of a bulb is ,

$P=V^2/R$

or $R=V^2/P$

for bulb $B_1$ , $R_1={18}^2/4.5=72\Omega$

for bulb $B_2$ , $R_1={18}^2/6.75=48\Omega$