Electric Power
Direct current
-Moves only in one direction, from positive terminal to negative terminal of a system -Current is not transferred efficiently a. direct currents are bad for transmitting electricity over long distances
4. How much does it cost to watch an entire World Series (21 h) on a 90.0 W black-and-white television set? Assume that electrical energy costs $0.070/kW*h
1 hour of 90 W = 0.09 kWh 0.09(21) = 1.89 kWh 1.89(0.070) = 0.1323 Answer = $0.13
P = I^2(R)
Energy loss is proportional to the square of the current in the wire.
Sample Problem E An electric space heater is connected across a 120 V outlet. The heater dissipates 1320 W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the heater.
Given: ΔV = 120 V P = 1320 W Unknown: R = ? Because power and potential difference are given but resistance is unknown, use the form of the power equation that relates power to the other two variables. P = (ΔV)^2 / R Rearrange the equation to solve for resistance. R = (ΔV)^2 / P = 120^2 / 1320 = 120^2 J^2 C^2 / 1320 J/s R = 120^2 J/C / 1320 C/s = 10.9 V/A R = 10.9 Ω
2. If the resistance of a light bulb is increased, how will the electrical energy used by the light bulb over the same period of time change?
It will mean that you can use the light bulb for less time as the electrical energy will be used quicker because of a lack of efficiency.
3. The potential difference across a resting neuron in the human body is about 70 mV, and the current in it is approximately 200μA. How much power does the neuron release?
P = IΔV P = 200(70) P = 14000 mcW P = 1 x 10^-5 W
What unit of measurement to electric companies use measure energy consumed?
kWh (KiloWattHour) 1 kWh = 3,600,000 Joules
2. A small electronic device is rated at 0.25 W when connected to 120 V. What is the resistance of this device?
ΔV = 120 V P = 0.25 W R = (ΔV)^2 / P R = 120^2 / 0.25 R = 14400 / 0.25 R = 5.8 x 10^4 Ω
1. A 1050 W electric toaster operates on a household circuit of 120 V. What is the resistance of the wire that makes up the heating element of the toaster?
ΔV = 120 V P = 1050 W R = (ΔV)^2 / P R = (120)^2 / 1050 R = 14400 / 1050 R = 14 Ω
5. What would the current in the heater in Problem 4 be if the wire developed a short and the resistance was reduced to 0.100 Ω?
ΔV = 50.0 V R = 0.100 Ω P = 2500 / 0.100 P = 25000 W P = IΔV 25000 = I(50) I = 5.00 x 10^2 A
Alternating current
-Current changes direction periodically -More efficient at transferring currents over long distances
4. An electric heater is operated by applying a potential difference of 50.0 V across a wire of total resistance 8.00 Ω. Find the current in the wire and the power rating of the heater.
ΔV = 50.0 V R = 8.00 Ω P = (ΔV)^2 / R P = (50)^2 / 8 P = 2500 / 8 P = 313 W
Power is related to current and potential difference by the equation...
P = IΔV Power = Current x Potential difference (aka voltage)
3. A calculator is rated at 0.10 W and has an internal resistance of 22 Ω. What battery potential difference is required for this device?
R = 22 Ω P = 0.10 W P = (ΔV)^2 / R 0.10 = (x)^2 / 22 x = 1.5 ΔV = 1.5 V