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.

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nuuk nuuk · Answer 1 · 2020-03-04T05:10:52+01:00

Answer:a

Explanation:

Given

Potential difference [tex]V=110\ V[/tex]

Power of bulb A [tex]P_A=60\ W[/tex]

Power of bulb B [tex]P_B=100\ W[/tex]

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

[tex]P=\dfrac{V^2}{R}[/tex]

[tex]P_A=\dfrac{(110)^2}{R_A}[/tex]

[tex]60=\dfrac{110^2}{R_A}[/tex]

[tex]R_A=201.66\ \Omega[/tex]

similarly

[tex]R_B=\dfrac{110^2}{100}[/tex]

[tex]R_B=121\ \Omega[/tex]

[tex]R_A>R_B[/tex]

so current in bulb A is smaller than B

Thus the 60 W bulb has a greater resistance.

Thus option (a) is correct