Question

14. A lightbulb is connected to a 120 V power source, forming a simple series circuit with one load.
The lightbulb has a resistance of 240 W and is left switched on for 6 hours.

a) What is the current that flows through the lightbulb? How many electrons pass through the bulb in the 6 hour period?   What is the power dissipated in the lightbulb? If a power company charges 8 cents / kW×h for electricity, how much would it cost you to run this bulb for 6 hours?

Answer 1

Given:

Voltage, V= 120 V

Resistance, R = 240 Ω

TIme duration, t = 6 hours = 6*60*60 = 21600 s

We know that Current, I = V/R

= 120/240

= 0.5 A

Now, Current is equal to the amount of charge passing per unit time

I = q/t

⇒ 0.5 = q/(21600)

⇒ q= 10800 C

Number of electrons passing

n = q / e Where e represents charge on a single electron

= 10800/(1.6*10^-19)

= 6.75*10²² electrons

Power dissipated

P = V² / R

= (120)²/240

60 W = 6*10^-2 kW

Cost to run the bulb for 6 hours

Cost = Charge*units used

= 8*6*10^-2*6

= 2.88 cents