# 20.4 Electric power and energy

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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?

Electric energy depends on both the voltage involved and the charge moved. This is expressed most simply as $\text{PE}=\text{qV}$ , where $q$ is the charge moved and $V$ 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

$P=\frac{\text{PE}}{t}=\frac{\text{qV}}{t}\text{.}$

Recognizing that current is $I=q/t$ (note that $\Delta t=t$ here), the expression for power becomes

$P=\text{IV.}$

Electric power ( $P$ ) 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, $\text{1 A}\cdot \text{V}=\text{1 W}$ . 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 $P=\text{IV}=\left(\text{20 A}\right)\left(\text{12 V}\right)=\text{240 W}$ . In some applications, electric power may be expressed as volt-amperes or even kilovolt-amperes ( $\text{1 kA}\cdot \text{V}=\text{1 kW}$ ).

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

$P=\text{IV}$
$P=\frac{{V}^{2}}{R}$
$P={I}^{2}R\text{.}$

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, $P$ can be the power dissipated by a single device and not the total power in the circuit.)

A soccer player kicked off a ball at velocity of 62 ft/s at angle 45°. A goal keeper is 43 yard away from the direction in which ball kicked off. At what minimum velocity he runs to meet the ball?
A soccer player kicked off the ball at the velocity of 62 ft/s at 45° with horizontal.A goal keeper is 43 yard away from the ball kicked position.At what minimum velocity he runs to meet the ball?
Ram
what is torque
The turning effect of force is called torque.
Uzair
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formula for impedance
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ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
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Alo
Alo
the time rate of increase in velocity is called
acceleration
Emma
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Victoria
Greetings,users of that wonderful app.
how to solve pressure?
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
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forces acting and lying on d same plane
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How does a current follow?
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
Abubakar
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akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH