Question

A 75 watt and a 100 watt light bulb, designed to be used with standard 120 V ac, are connected in a series across a 120 V ac potential difference. The power output is......

greater for the 100 W bulb

greater for the 75 W bulb

same for both bulbs

Answer 1

greater for the 75 W bulb

let P1 = 75 W

P2 = 100 W

V_rms = 120 V

let R1 and R2 are the resiatnces of the bulbs.

use, P1 = V^2/R1

R1 = V^2/P1

= 120^2/75

= 192 ohms

similarly, R2 = V^2/P2

= 120^2/100

= 144 ohms

when both are connected in series, Req = R1 + R2

= 192 + 144

= 336 ohms

current through both bulbs, I1 = I2 = V/Req

= 120/336

= 0.3571 A

power at bulb 1, P1 = I1^2*R1

= 0.3571^2*192

= 24.5 W

power at bulb 2, P2 = I2^2*R1

= 0.3571^2*144

= 18.4 W

clearly, P2 < P1