 # Unit 6: Energy and Power

In this unit you’ll study the closely related topics of energy and pwer.

##### Work and Energy
• In physics, work is the expenditure of energy to overcome a restraint or to achieve a change in the physical state of a body.
• Energy is the ability to do work.
• We use the symbol W to stand for either energy or work.
• Energy comes in many forms. A few of these are:
• heat energy
• light energy
• sound energy
• mechanical energy
• chemical energy
• electrical energy.
• Many everyday devices convert energy from one form to another. For example:
• A loudspeaker converts electrical energy to sound energy.
• A toaster converts electrical energy to heat energy.
• A light bulb or LED converts electrical energy to light energy.
• Energy is measured in units called joules. We use the symbol J to stand for the joule.
• To give you some idea of how much energy is in 1 joule, you’d need about 90 kJ of heat energy to boil a cup of water that starts out at room temperature.
##### Power
• Power, abbreviated P, is the rate at which energy is spent.
• In other words, power is the amount of energy that’s used in a given amount of time, or energy per time. In equation form, that’s

P = W ÷ t

• Since energy is measured in joules, and time is measured in seconds, power will be measured in joules per second. The unit of joules per second is given a special name, watt. We use the symbol W to stand for the watt.
• If you’ve ever changed a light bulb, you’re probably familiar with the word "watt." Now you know that the number of watts tells you the bulb’s power, or how quickly the bulb uses energy. For instance, a 120-watt light bulb uses energy twice as fast as a 60-watt bulb.
• Many circuits use small amounts of power, measured in milliwatts (mW) or microwatts (µW).
• At the other extreme, utility companies and radio broadcasting stations use huge amounts of power, measured in kilowatts (kW) or megawatts (MW).
• ##### W versus W
• Be careful not to confuse W, the symbol for energy, with W, the symbol for watts.
• This distinction follows the rule that you learned earlier, which says that we generally use italic letters to stand for quantities and non-italic letters to stand for units. Energy (W) is a quantity, while the watt (W) is a unit. But the watt is the unit of power, not of energy. This can be confusing, so be on you toes!
• From time to time you should go back and review our table of units and quantities given in Unit 1.
##### Kilowatt-hours
• We’ve seen that energy is measured in joules and power is measured in watts, and that 1 watt equals 1 joule per second. These units are convenient for low-power situations. In the electrical power industry, which deals with enormous quantities of energy and power, it’s more convenient to use larger units, namely the kilowatt (for power) and the kilowatt-hour (for energy).
• As you can guess, one kilowatt is equal to a thousand watts: 1 kW = 1000 W.
• One kilowatt-hour is the amount of energy consumed in 1 hour when the rate of consumption is 1 kW.
• Remember the equation above that relates energy, power, and time: P = W ÷ t.
• If we rearrange this to solve for energy, we get

W = P × t

• In words, this says that energy equals power times time. When you use this equation, if P is in watts and t is in seconds, then your answer (W) will be in joules. But if P is in kilowatts and t is in hours, then your answer (W) will be in kilowatt-hours.
• The electric company charges you by the kilowatt-hour for the electricity that you use. If you study your monthly electric bill, you will find the number of kilowatt-hours that you used during the month, along with the price per kilowatt-hour.
• ##### Power Formulas
• When current flows through resistance, electric energy is converted to heat energy.
• The rate of this energy conversion is the power. (Remember, power equals energy per time.) This energy conversion takes place at a rate that depends on the size of the resistance and the current through it:

P = I2 × R

• Here are two other useful expressions for power, which we can derive from the one above by using Ohm’s law and a little algebra:

P = I × V

P = V2 ÷ R

• In each of these equations, R is the size (in ohms) of the resistance, V is the voltage (in volts) across the resistance, and I is the current (in amps) through the resistance.
• The three formulas will always give the same answer. Use whichever one is most convenient. For example, suppose you know a resistor’s voltage and its current, and you want to figure out its power. You could use Ohm’s law to figure out the resistance, and then use P = I × V to compute the power. But it would be easier just to use P = V2 ÷ R, which saves you from having to figure out the resistance first.
• Using a fancy term, we say that P is the power dissipated in the resistance.
• • ##### The Power Wheel
• The power formulas and Ohm’s law give us the relationships among four quantities: voltage (V), current (I), resistance (R), and power (P).
• It turns out that, by using these equations, whenever you know the value of any two of these quantities, you can solve for the other two quantities.
• For example, if you kow a resistor’s voltage and its power, then you can also figure out its current and its resistance, by using Ohm’s law and the power formulas.
• When I’m doing a problem like this, I prefer just to remember Ohm’s law and the power formulas, and then use them on a case-by-case basis to solve for whichever quantities I’m looking for.
• But many people like to use a device called the power wheel, which summarizes all of these formulas in all the different ways they can be rearranged. The power wheel looks like this: • Note that the wheel is divided into four quadrants, one for each quantity. The formulas in each quadrant give you different ways to calcualte that quantity. For example, to calculate voltage (upper-right quadrant) you can use V = P ÷ I, or you can use V = × R, or you can use V = √(P × R).
• • ##### Resistor Power Ratings
• A resistor’s power rating. is the maximum amount of power that the resistor can dissipate without being damaged by excessive heat.
• A resistor’s physical size is related not to its resistance value, but rather to its power rating. In general, larger resistors (in physical size, not in ohms) can handle more power than smaller resistors.
• Standard power ratings of resistors include 1/8 watt, 1/4 watt, 1/2 watt, 1 watt, and 2 watt.
• Example: The photograph below shows four resistors whose power ratings are (from top to bottom) 1/4 W, 1/2 W, 1 W, and 2 W. The 2-W resistor is about one inch long. (Click the picture for a larger photo.) • The next photograph, drawn to a different scale, shows two high-power resistors. At the bottom of the photo is a 1/4-watt resistor (same as the smallest one in the photo above). Above it is a 75-watt resistor, and above that is a 225-watt resistor. This 225-watt resistor is about eleven inches long. As you can see, to handle lots of power, a resistor has to be big. ##### Power Rating Must Not Be Exceeded
• If a resistor’s power rating is too small for the amount of heat produced by the current flowing through it, the resistor may be damaged or destroyed. In particular, its resistance value may be greatly altered, or it may even "burn out" and become an open. If you use a multimeter to measure a burnt-out resistor’s resistance, you’ll get an over-range reading on every range.
• When you’re designing or building a circuit, you should use a resistor whose power rating is greater than the actual amount of power that you expect the resistor to dissipate.
• Example: Suppose a resistor in a particular circuit must be able to withstand a current of 35 mA and a voltage drop of 10 V. Then the power dissipated by that resistor would be 350 mW. (That’s P = V×I.) Therefore, in building this circuit, we would need to use a resistor with a power rating greater than 350 mW. So we could not use a 1/8 watt (which is the same as 125 mW) or a 1/4 watt (the same as 250 mW) resistor. The smallest standard size that we could use is 1/2 W (the same as 500 mW).
• ##### Voltage Drop
• A resistor heats up whenever current passes through it, because the electrons carrying the current collide with the resistor’s atoms. This heat is given off to the surrounding air, which means that energy is being lost from the circuit to its environment.
• From your lab work, you’re familiar with the idea of measuring the voltage across a resistor in a circuit. We refer to this as the resistor’s voltage drop. This voltage drop indicates how much energy electrons are losing (through heat loss) as they pass through the resistor.

##### Power Supplies
• A power supply is a device that provides electrical power.
• One example of a power supply is a battery, which converts chemical energy to electrical energy.
• Another example is an electronic power supply, which converts one type of electrical energy into another type. For instance, the DC power supply on a trainer in our lab converts the wall socket’s 110-V AC electricity into DC electricity at a much lower voltage (up to 15 V). ##### Input Power and Output Power
• Any device that uses electricity to perform some useful function does so by converting energy from one form to another. For example (as already mentioned):
• A loudspeaker converts electrical energy to sound energy.
• A toaster converts electrical energy to heat energy.
• A light bulb or LED converts electrical energy to light energy.
• A battery converts chemical energy to electrical energy.
• An electronic power supply converts electrical energy in one form to electrical energy in another form.
• The energy supplied to achieve a desired outcome is called the input energy, abbreviated WIN, and the modified form of energy that represents the outcome is the output energy, abbreviated WOUT.
• Input power, abbreviated PIN, is the rate at which a device uses input energy, and output power, abbreviated POUT, is the rate at which the device produces output energy.
• A basic law of physics says that a device’s output power cannot be greater than its input power.
##### Efficiency
• Efficiency is defined to be the ratio of output power to input power:

Efficiency = η = POUT ÷ PIN

• Note that the symbol for efficiency is the Greek letter η, which is called eta (pronounced like "ate-uh"). This letter looks a bit like our letter n, but it’s not the same.
• Efficiency is a pure number. It doesn’t have units of joules or watts or any other unit.
• Efficiency is often expressed as a percentage. For instance, if the equation above gives an answer of 0.567, you could express this as 56.7%.
• As noted above, a device’s output power cannot be greater than its input power. Therefore, no device can have an efficiency greater than 1 (or 100%).
• The difference between input power and output power is called power loss:

PLOSS = POUTPIN

• ##### Unit 6 Review

Congratulations! You’ve completed the e-Lesson for this unit.