Power in Circuits

Concept: Power in Circuits

Video Transcript

Hey guy. In this video we're going to be talking about the power generated by circuits, alright? Let's get to it. Remember that resistance is the internal friction within conductors as electrons pass through them, okay? This means that energy is lost, okay? If you see the word dissipated, dissipated is another term used to describe energy loss, okay? Remember, that as an object slides over a surface with friction that object loses kinetic energy, right? It slows down similarly as electrons bounce in between the atoms within a conductor, those collisions are causing the electrons to lose energy, okay? How much energy is lost through a resistor? Well, if the resistor is at some sort of potential difference, a voltage of V, then the energy as an electron passes through it's just the charge of that electron times V, okay? That's a very straightforward application, all of the our energy equations from electrostatics, okay? If an electron passes through a resistor of 2 volts of voltage, how much energy does the electron lose passing through this resistor, okay? U is going to be q, V. Now, don't worry about the sign here, we're talking about energy lost, right? We already know that that energy is lost, we just want to know the amount that is lost, okay? So, we're just going to say it's the magnitude of this, the charge of an electron is just the elementary charge and we're saying it's 2 volts, so this is 3.2 times 10 to the negative 19 joules, that is how much energy is lost, and we know as the electron passes through the resistor it's always going to lose energy, okay? So, there's never going to be a question of how much energy is gained as the electron passes through the resistor, okay? Now, remember that energy lost per second is always going to be called the power output, right? If you are losing energy you are releasing it into the environment, this is a power output, where the power is defined as the change in energy over time, okay? The amount of energy released over time, the power output of any circuit element. So, no matter what it is within the circuit, it could be a battery, it could be a resistor, it could be anything is always V times i. Now, specifically for resistor because of Ohm's law V equals i, R, we can form two more variations of that above equation, we can say i squared R is the power or V squared over R, okay? This equation right here, our general equation for the power, is sometimes called joules law, okay? It's the same Joule as the unit for energy.

Now, a battery operates at a voltage of 9 volts, if the battery is outputting 500 watts of energy, how much occurring is the battery producing, okay? This is a straightforward application of joules law, we want to find the current. So, we have to divide the voltage over, so the current is just the power divided by the voltage, which is 500 Watts over 9 volts, which is 55.6 amps of current, that that battery is outputting, okay? Pretty straightforward, pretty simple. Alright guys, that wraps up our discussion of power in circuits, thanks for watching.

Problem: A hair dryer operates at 120 V (the voltage produced by a household outlet), and outputs 1200 W of energy. For this problem, treat the hair dryer as a single resistor. 

(a) At what current does the hair dryer operate?
(b) What is the resistance of the hair dryer?


Problem: An incandescent lightbulb produces 100 W of light. If this lightbulb operates at 25% efficiency (meaning that out of all the power it generates, only 25% is released as light), what resistance must the lightbulb have if it operates at 120 V?


Power in Circuits Additional Practice Problems

A car's battery produces 12 V and has a charge of 70 A*hr. How long could the battery run a car whose entire electronic system had an equivalent resistance of 5 Ω? This assumes that the alternator isn't recharging the battery as you drive.

Watch Solution

For most materials, the resistance is actually temperature dependent, and typically increases as temperature rises. For this problem, however, let's assume a very simple (if not physical) case. A 100 Ω resistor with a mass of 0.15 kg is connected to a 120 V power source. So long as the temperature is below 1000°C, the resistance remains 100 Ω, but once it rises above 1000°C, the resistance immediately becomes infinite, and the circuit can no longer operate. How long could this circuit run? The specific heat of the resistor we are considering is 50 J/g*K and we will assume the resistor begins at room temperature, about 23°C.

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A 1500 W hair dyer is designed to be used with an electrical outlet that provides 115 V. What current does the hair dryer draw from the outlet?

a. 0.8 A

b. 13 A

c. 3.6 A

d. 12 A

Watch Solution

The resistivity of gold is 2.44 x 10 -8 Ω•m at a temperature of 20°C. A gold wire, 1.4 mm in diameter and 17 cm long, carries a current of 190 ma. The power dissipated in the wire is closest to:

A) 0.043 mW

B) 0.079 mW

C) 0.061 mW

D) 0.024 mW

E) 0.097 mW

Watch Solution

The resistivity of gold is 2.44 x 10 -8 Ω•m at a temperature of 20°C. A gold wire, 1.8 mm in diameter and 14 cm long, carries a current of 480 ma. The power dissipated in the wire is closest to:

A) 0.077 mW

B) 0.25 mW

C) 0.14 mW

D) 0.19 mW

E) 0.31 mW

Watch Solution

Which bulb will be the brightest if connected in series? The voltages and wattages shown in the graphs are their nominal settings, not actual values when connected in series.

A) 60 W bulb

B) 120 W bulb

C) 240 W bulb

D) Equally bright

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Four identical resistors are connected in series to an ideal battery. The total power supplied by the battery is 10 W. The same resistors are then connected to the same battery in parallel. What is the total power supplied by the battery in this new, parallel configuration?

A) 0.6 W

B) 2.5 W

C) 40 W

D) 160 W

E) It is impossible to say with the given information.

Watch Solution

A 200-W light bulb is connected across 110 V. What current will flow through this bulb?

A) 0.9 A

B) 0 A

C) 0.6 A

D) 1.8 A

Watch Solution