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Have you ever noticed that how much electrical energy is consumed by

electrical appliances in your home. Make a chart of all of these appliances with their

power in kW and an average use on daily, weekly, and monthly basis. Usually the

electrical power is written on most of the appliances or on their packing. Calculate

the total consumption of electrical energy in kWh in your home for December, 2020.

Find the expected electricity bill for this month, if 1 kWh energy costs Rs 10. Which

item consumed most energy during the month?

## Answers

**Answer:**

LEARNING OBJECTIVES

By the end of this section, you will be able to:

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 Figure 1(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.

Figure 1. (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, 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

=

P

E

t

=

q

V

t

.

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

P = 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, 1 A ⋅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). To see the relationship of power to resistance, we combine Ohm’s law with P = IV. Substituting I = V/R gives P = (V/R)V=V2/R. Similarly, substituting V = IR gives P = I(IR) = I2R. Three expressions for electric power are listed together here for convenience: