Light bulb A is marked \"50.0 W 120 V,\" arid light bulb B is marked \"100.0 W 1

Question

Light bulb A is marked "50.0 W 120 V," arid light bulb B is marked "100.0 W 120 V." These labels mean that each bulb has its respective power delivered to it when it is connected to a constant 120 V source. Find the resistance of each bulb. During what time interval does 2.0 C pass into bulb A? Is this charge different upon its exit versus its entry into the bulb? Explain. In what time interval does 1.0 J pass into bulb A? By what mechanisms does this energy enter and exit the bulb? Explain. Find the cost of running both light bulbs continuously for 30.0 days, assuming the consumer energy department sells its product at $0. 150 per kWh.

Explanation / Answer

A)

(W = V^2 / Omega)

So,

(Omega = V^2 / W)

So, for bulb A,

120^2/50 = 288 Ohms

And for bulb B

120^2 / 100 = 144 Ohms

B)

An ampere (A) is the measure of current

It is measured in Coulomb's per second. A= C/s

W = V*A, so A = W/V

Thus, for bulb a, the current is:

I= 50 / 120 = 0.416667 Amps = 0.416667 C/s

Now we do a little dimensional analysis:

2.0 C * 1 s / 0.4166667 C = 4.80 s

C)

No. The potential changes across a circuit, but the charge remains constant.

D)

1 Joule = 1 Coulomb * 1 Volt

Joules / second = Coulombs / second * Volts

J / s = 0.416667 C/s * 120 V

J/s = 0.4166667 * 120

Again, some dimensional analysis...

1.0 J * 1 s / (0.4166667 * 120) J = .0020 s

E) It enters by movement of charged particle from an area of higher to lower electric potential. This energy is transfered by the lightbulb into light and heat.

F) 30 days is 30*24 = 720 hours

For lightbulb A,

50 W* 720 h = 36000 Watt hours = 36kWh

$0.150 / 1 kWh * 36 kWh = $5.40

For lightbulb B,

100 W*720 h = 7200 Watt hours = 72kWh

$0.150 / 1 kWh * 72 kWh = $10.80

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