A 4-W night-light is plugged into a 120-V circuit and operates continuosly for 1 year.?

Question

How much current does it draw? What is the resistance of its fillament? How much energy is consumed in a year? What is the cost of its operation for a year at the utility rate of 15 cents/kWh?

Answer 1

Ohm's Law:
V = R * I

Power = Energy / time
Power = V * I

Where V is the voltage, R is the resistance, and I is the current.


We know the light has a power of 4 watts. We also know the voltage through the light (120 v). From this we can calculate the current through the right.
P = V * I
4 watts = (120 volts) * I
Solving for I, we get,
I = (4 watts) / (120 volts) = .0333 amps

I = .0333 amps

We now know both the voltage and the current through the lightt. Using Ohm's law we can calculate the resistance.
V = RI
(120 v) = R * (.0333 amps),
Solving for R,
R = (120 v) / (.0333 amps) = 3600 Ohms

R = 3600 Ohms

We know the power of the bulb and we are asked to find the energy consumed per year. For every 1000 hours the ligh is left on, the light consumes 4 kWh of energy (at a rate of 4 watts)
In 1 year there are (24 h/day * 365 days) hours (= 8760 hours).
Power = Energy / time
Energy = Power * time
Energy = (4 watts) * (8760 hours)
Energy = 35040 Wh,
divide by 1000 to get kWh,
Energy = 35.04 kWh

At a rate of 15 cents per kWh the energy will cost,
cost = Energy * rate
cost = (35.04 kWh) * (15 cents / kWh)
cost = $5.26

Answer 2

Here are the basic equations that you need, I'll walk you through it, but not give the answer -- you have to do the calculations.

step 1.
Watts = Volts * Amps (Amps is the measure of current)
4W = 120V * ???Amps

step 2.
Volts = Amps * Ohms (Ohms is resistance)
120V = ???Amps * ??? Ohms resistance of filiment.
Use ???Amps from step 1.

step 3.
Energy (Joules) = Watts * time (seconds)
Energy (kWhr) = Watts/1000 * time (hours)
(kWhr is kiloWatt-hours)
How many hours in one year? 24 hours in a day * 365 days in a year, and it's a 4Watt bulb, so
Energy (kWhr) = 4/1000 * number of hours in 1 year.

Step 4.
To get the cost, just multiply 15 cents/kWhr * the Energy from step 3.

Answer 3

The potency in W is the current (in A) times the voltage (V).
P = i U
so 4 = i x 120 or i = 4/120 = 0.033 A
The resistance can be reached doing U = Ri,
or R = U/i = 3600 ohms
the energy is the potency times time. E = Pt
so E = 4W x 1year = 4W x 365days = 4W x 8760h = 35040 Wh
or E = 35,04 kWh
The cost is 35,04 x $0,15 = $5,26