Understanding Power, Resistance, and Current in Light Bulbs

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.

Question:

Which statement is correct regarding the power, resistance, and current of the two light bulbs?

Answer:

Answer: a

Explanation:

Given:

Potential difference V = 110 V

Power of bulb A PA = 60 W

Power of bulb B PB = 100 W

If voltage is the same for both bulbs, then power is given by

P = V^2 / R

PA = 110^2 / RA

60 = 110^2 / RA

RA = 201.66 Ω

Similarly,

RB = 110^2 / 100

RB = 121 Ω

RA > RB

So, the current in bulb A is smaller than in bulb B

Thus, the 60 W bulb has a greater resistance.

Therefore, option (a) is correct.