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  • Calculate the power dissipated by a resistor and power supplied by a power supply.
  • Calculate the cost of electricity under various circumstances.

Power in electric circuits

Power is associated by many people with electricity. Knowing that power is the rate of energy use or energy conversion, what is the expression for electric power    ? Power transmission lines might come to mind. We also think of lightbulbs in terms of their power ratings in watts. Let us compare a 25-W bulb with a 60-W bulb. (See [link] (a).) Since both operate on the same voltage, the 60-W bulb must draw more current to have a greater power rating. Thus the 60-W bulb’s resistance must be lower than that of a 25-W bulb. If we increase voltage, we also increase power. For example, when a 25-W bulb that is designed to operate on 120 V is connected to 240 V, it briefly glows very brightly and then burns out. Precisely how are voltage, current, and resistance related to electric power?

Part a has two images. The image on the left is a photograph of a twenty five watt incandescent bulb emitting a dim, yellowish white color. The image on the right is a photograph of a sixty watt incandescent bulb emitting a brighter white light. Part b is a single photograph of a compact fluorescent lightbulb glowing in bright pure white color.
(a) Which of these lightbulbs, the 25-W bulb (upper left) or the 60-W bulb (upper right), has the higher resistance? Which draws more current? Which uses the most energy? Can you tell from the color that the 25-W filament is cooler? Is the brighter bulb a different color and if so why? (credits: Dickbauch, Wikimedia Commons; Greg Westfall, Flickr) (b) This compact fluorescent light (CFL) puts out the same intensity of light as the 60-W bulb, but at 1/4 to 1/10 the input power. (credit: dbgg1979, Flickr)

Electric energy depends on both the voltage involved and the charge moved. This is expressed most simply as PE = qV size 12{"PE"= ital "qV"} {} , where q size 12{q} {} is the charge moved and V size 12{V} {} is the voltage (or more precisely, the potential difference the charge moves through). Power is the rate at which energy is moved, and so electric power is

P = PE t = qV t . size 12{P = { { ital "PE"} over {t} } = { { ital "qV"} over {t} } "."} {}

Recognizing that current is I = q / t size 12{I = q/t} {} (note that Δ t = t size 12{Δt=t} {} here), the expression for power becomes

P = IV. size 12{P = ital "IV."} {}

Electric power ( P size 12{P} {} ) is simply the product of current times voltage. Power has familiar units of watts. Since the SI unit for potential energy (PE) is the joule, power has units of joules per second, or watts. Thus, 1 A V = 1 W size 12{"1 A " cdot V=" 1 W"} {} . For example, cars often have one or more auxiliary power outlets with which you can charge a cell phone or other electronic devices. These outlets may be rated at 20 A, so that the circuit can deliver a maximum power P = IV = ( 20 A ) ( 12 V ) = 240 W . In some applications, electric power may be expressed as volt-amperes or even kilovolt-amperes ( 1 kA V = 1 kW size 12{"1 kA " cdot V=" 1 kW"} {} ).

To see the relationship of power to resistance, we combine Ohm’s law with P = IV size 12{P = ital "IV"} {} . Substituting I = V/R size 12{I = ital "V/R"} {} gives P = ( V / R ) V = V 2 / R size 12{P = \( V/R \) V=V rSup { size 8{2} } R} {} . Similarly, substituting V = IR size 12{V= ital "IR"} {} gives P = I ( IR ) = I 2 R size 12{P =I \( ital "IR" \) = I rSup { size 8{2} } R} {} . Three expressions for electric power are listed together here for convenience:

P = IV size 12{P = ital "IV"} {}
P = V 2 R size 12{P = { {V rSup { size 8{2} } } over {R} } } {}
P = I 2 R . size 12{P = I rSup { size 8{2} } R"."} {}

Note that the first equation is always valid, whereas the other two can be used only for resistors. In a simple circuit, with one voltage source and a single resistor, the power supplied by the voltage source and that dissipated by the resistor are identical. (In more complicated circuits, P size 12{P} {} can be the power dissipated by a single device and not the total power in the circuit.)

Questions & Answers

Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic
sam Reply
who is a nurse
Chilekwa Reply
A nurse is a person who takes care of the sick
Bukola
a nurse is also like an assistant to the doctor
Gadjawa
explain me wheatstone bridge
Malik Reply
good app
samuel
Wheatstone bridge is an instrument used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
MUHD
Rockwell Software is Rockwell Automation’s "Retro Encabulator". Now, basically the only new principle involved is that instead of power being generated by the relative motion of conductors and fluxes, it’s produced by the modial interaction of magneto-reluctance and capacitive diractance. The origin
Chip
what refractive index
Adjah Reply
write a comprehensive note on primary colours
Harrison Reply
relationship between refractive index, angle of minimum deviation and angle of prism
Harrison
Who knows the formula for binding energy,and what each variable or notation stands for?
Agina Reply
1. A black thermocouple measures the temperature in the chamber with black walls.if the air around the thermocouple is 200 C,the walls are at 1000 C,and the heat transfer constant is 15.compute the temperature gradient
Tikiso Reply
what is the relationship between G and g
Olaiya Reply
G is the u. constant, as g stands for grav, accelerate at a discreet point
Mark
Is that all about it?
Olaiya
pls explain in details
Olaiya
G is a universal constant
Mark
g stands for the gravitational acceleration point. hope this helps you.
Mark
balloon TD is at a gravitational acceleration at a specific point
Mark
I'm sorry this doesn't take dictation very well.
Mark
Can anyone explain the Hooke's law of elasticity?
Olaiya Reply
extension of a spring is proportional to the force applied so long as the force applied does not exceed the springs capacity according to my textbook
Amber
does this help?
Amber
Yes, thanks
Olaiya
so any solid can be compressed how compressed is dependent upon how much force is applied F=deltaL
Amber
sorry, the equation is F=KdeltaL delta is the triangle symbol and L is length so the change in length is proportional to amount of Force applied I believe that is what Hookes law means. anyone catch any mistakes here please correct me :)
Amber
I think it is used only for solids and not liquids, isn't it?
Olaiya
basically as long as you dont exceed the elastic limit the object should return to it original form but if you exceed this limit the object will not return to original shape as it will break
Amber
Thanks for the explanation
Olaiya
yh, liquids don't apply here, that should be viscosity
Chiamaka
hope it helps 😅
Amber
also, an object doesnt have to break necessarily, but it will have a new form :)
Amber
Yes
Olaiya
yeah, I think it is for solids but maybe there is a variation for liquids? that I am not sure of
Amber
ok
Olaiya
good luck!
Amber
Same
Olaiya
aplease i need a help on spcific latent heat of vibrations
Bilgate
specific latent heat of vaporisation
Bilgate
how many kilometers makes a mile
Margaret Reply
about 1.6 kilometres.
Faizyab
near about 1.67 kilometers
Aakash
equal to 1.609344 kilometers.
MUHD
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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