A three-way light bulb is a bulb that shines with three different blight nesses,

Question

A three-way light bulb is a bulb that shines with three different blight nesses, depending on the position of a switch. One way to make a three way light bulb is to allow connections to the bulb filament so that, when the switch is in the position labeled "1", the 120 V from the wall socket is connected across the entire filament; in the position labeled "2", the 120 V is connected across 40% of the length of the filament; and in the position labeled "3", the 120 V is connected across the remaining 60% of the length of the filament. Assume the filament has a uniform cross-section, and that the resistance of the filament Is Independent of the filament's temperature. Rank the switch positions based on the brightness of the bulb, from brightest to dimmest. (Use only or "=" symbols. Do not include any parentheses around the letters or symbols.) If the bulb dissipates 48.0 W when the switch is in the position labeled "1", how much power is dissipated when the switch is in the position labeled "3"?

Explanation / Answer

here,

resistance = p * L/area

so resistance is directly proportional to the length

a)

if l is the length of filamemt

l1 = l

l2 = 0.4 * l

l3 = 0.6 * l

as resistance is directly proportional to the length

R1 > R3 > R2

potential difference is constant ,

bulb will be brighter as per the current through it

so, I2 > I3 > I1

the sequence of brightness is (2 > 3 > 1)

b)

Power for 1 , P1 = 48 V

power , P = V^2 /R

so,

P3 /P1 = ( V^2/R3 ) /(V^2 /R1)

P3 /P1 = R1 /R3 = l1/l3

P3/48 = 1/0.6

P3 = 80 W

power through bulb 3 is 80 W

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