Question

Two light bulbs are operated at a potential difference of 110 V. Light bulb A produces 60 W of power and light bulb B produces 100 W of power. Which statement below is correct?
a. The 60 W bulb has a greater resistance and smaller current than the 100 W bulb.

b. The 60 W bulb has a smaller resistance and smaller current than the 100 W bulb.

c. The 60 W bulb has a greater resistance and greater current than the 100 W bulb.

d. The 60 W bulb has a smaller resistance and greater current than the 100 W bulb.

Answer 1

Answer:a

Explanation:

Given

Potential difference $V=110\ V$

Power of bulb A $P_A=60\ W$

Power of bulb B $P_B=100\ W$

If voltage is same for both the bulbs then Power is given by

$P=\dfrac{V^2}{R}$

$P_A=\dfrac{(110)^2}{R_A}$

$60=\dfrac{110^2}{R_A}$

$R_A=201.66\ \Omega$

similarly

$R_B=\dfrac{110^2}{100}$

$R_B=121\ \Omega$

$R_A>R_B$

so current in bulb A is smaller than B

Thus the 60 W bulb has a greater resistance.

Thus option (a) is correct