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.