A 25W 120V light bulb and a 150W 120V light bulb are connect

A 25-W, 120-V light bulb and a 150-W, 120-V light bulb are connected in series across a 240-V line. Assume that the resistance of each bulb does not vary with current. (Note: This description of a light bulb gives the power it dissipates when connected to the stated potential difference; that is, a 25-W, 120-V light bulb dissipates 25 W when connected to a 120-V line.)

a) Fund the current through the bulbs.

b) Find the power dissipated ein each bulb.

c) One bulb burns out very quickly. Which one? Why?

Solution

here,

for 25W, 120 V

let the resistance be R1

P = V^2 /R1

R1 = 120^2 /25 = 576 ohm

for 150 W, 120 V

let the resistance be R2

P = V^2 /R2

R2 = 120^2 /150 = 96 ohm

a)

the current through the bulbs , I = 240/( R1 + R2)

I = 240 /( 576 + 96) A

I = 0.36 A

b)

the power dissapated in 1 , P1 = I^2 * R1 = 73.5 W

the power dissapated in 2 , P2 = I^2 * R2 = 12.4 W

c)

as the power dissapated in first bulb is more than the rated power

so, first bulb will run very quickly