Chapter 23 |

Current events...

Electric current

Water current is simply how much water passes per second. Electrical current is similar; in this case, it is the flow of electrons per second. One Ampere is defined as 1 Coulomb of charge per second. One Coulomb is equal to about 6.25 billion billion electrons. (No, that wasn't a typo...)

A current of 0.5 A flows through a light bulb for 1 minute. How much charge flowed during this time?

How fast are those electrons moving? In a typical current in your household:

A) At the speed of light.

B) As fast as a supersonic jet.

C) As fast as a racecar.

D) As fast as a person walks.

E) As fast as a snail crawls.

Yeah, that's pretty slow. Then why does the light turn on so fast when you flip the switch?

Current is electrons moving through a substance, typically in a wire for our purposes. What makes the electrons move? To answer that, we need to review what we learned about electric potential.

Why is the water stored so high up? It took work to lift it up there. That work is stored as potential energy. When the water is allowed to flow down a pipe and out, it is moving fast because the potential energy has been converted to kinetic energy. Notice what matters here is the difference of the height at which it was stored and the height at which it is used.

Similarly, when charges have been separated, work was done. The stored energy per charge is the electric potential difference or sometimes just called the potential.

Consider a whole field of water balloons. The ones thrown the highest will be moving the fastest when they come back down.

Now consider two water tanks. Water from the tank that was raised higher will be moving faster when it exits the pipe. Similarly, if we put more work into separating charges, we will give them greater potential. The charges with higher potential will be moving faster when we let them go in the completed circuit, if everything else is held to be the same.

current analogy demo - water flow

Now we need to consider resistance. Think of resistance as something that tends to slow down the current, like constricting the diameter of the water pipe. The more resistance you give the circuit, the lower the current will be. A good conductor has low resistance. A good insulator has very high resistance. A semiconductor falls between the two. Resistance is measured in Ohms, and is given the symbol Ω.

Ohm's Law

Ohm's Law gives a very simple relationship between Voltage, current and resistance:

current analogy demo - marble and pins

Voltage = current x resistance

Volts = Amps x Ohms

How much current will flow through a light bulb that has a resistance of 60 Ω when it is connected to a 12 V battery?

What is the resistance of a toaster that draws 12 A when connected to a 120 V circuit?

Which of these configurations will light the bulb?

What is the ratio of the currents of these two circuits?

What is the ratio of the currents of these two circuits?

Series and parallel circuits

Electrons gain energy when they pass through the battery. They must lose all of their energy by the time they get back to the battery. Series circuits are those where the components of the circuit lie along the same path. The electrons lose energy (Voltage drop) each time they move through the filament of a light bulb. In a parallel circuit, each branch has a separate path to the battery. This means that each branch of a parallel circuit has the same voltage difference. In other words, the Voltage drop is equal across parallel branches.

Resistance increases as bulbs or resistors are connected in series. Resistance decreases as bulbs or resistors are connected in parallel.

This cutaway diagram of a light bulb illustrates how the wires are connected through the filament.

AC and DC current

There are two types of current, direct current (DC) and alternating current (AC). For direct current, the electrons simply flow along the wire. This is the kind of current you get in a circuit where a battery is the power source. With alternating current, electrons flow one way, then switch and flow back the other way, then switch again, etc. This switching happens many times per second, at a frequency of 60 Hz in the US. We use this method for carrying current over long distances because it is easy to use transformers to step up and step down the voltages. This means that power can be transported at high voltage and then stepped down for use in your home. Standard AC voltage is 120 V in the US. This is actually the root mean square (rms) value. The true amplitude is actually about 170 V.

Many appliances are made to use DC current, however, so the AC current coming in must be converted to DC. We do that using a diode and a capacitor. A diode is a one-way gate which only allows current to pass in just one direction. The resulting output is a pulsating DC current. Using two diodes catches all of the AC current. A capacitor can be added that will smooth out the current by slowly charging and discharging.

Electric power

An electron moving through a circuit has some potential energy, imparted to it from the power source. It suffers a voltage drop as it passes through a component like a resistor or a light bulb. We define the power as the product of current and voltage.

Power = current x voltage

Watts (J/sec) = Amperes (C/sec) x Volts (J/C)

1 kW = 1000 W = 1000 J/s. 1 kW-hr = 1000 J/s x 3600 s = 3,600,000 J

P = I x V = (V/R) x V = V^{2}/R = I^{2} x R

If a 120-V line to a socket is limited to 15 A by a safety fuse (or circuit breaker), will it operate a 1200-W hair dryer? Will it operate two hair dryers?

At 10¢/kW-hr, what does it cost to operate the 1200-W hair dryer for 1 hr?

Assume the bulbs are identical. What will be the relative order of brightness of the bulbs in each of these circuits?

Assume the bulbs are identical. What will be the relative order of brightness of the bulbs in each of these circuits?

Problems

1) If an electric current flows from one object to another what can we say about the relative magnitudes of the electric potentials of the two objects?

2) Is a current-carrying wire electrically charged?

3) Sometimes you hear someone say that a particular appliance "uses up" electricity. What is it that the appliance actually uses up and what becomes of it?

4) An electron moving in a wire collides again and again with atoms and travels an average distance between collisions that is called the mean free path. If the mean free path is less in some metals, what can you say about the resistance of these metals? For a given conductor, what can you do to lengthen the mean free path?

5) Why is the current in an incandescent bulb greater immediately after it is turned on, than it is a few moments later?

6) A simple lie detector consists of an electric circuit, one part of which is part of your body--like from one finger to another. A sensitive meter shows the current that flows when a small voltage is applied. How does this technique indicate that a person is lying? (And when does this technique not tell when someone is lying?)

7) If a current of one- or two-tenths of an ampere flows into one of your hands and out the other, you will probably be electrocuted. But if the same current flows into your hand and out the elbow above the same hand, you can survive even though the current may be large enough to burn your flesh. Explain.

8) Are automobile headlights wired in parallel or in series?

9) Estimate the number of electrons that a power company delivers annually to the homes of a typical city of 50,000 people.

10) If electrons flow very slowly through a circuit, why does it not take a noticeably long time for a lamp to glow when you turn on a distant switch?

11) Rearrange the equation Current = voltage/resistance to express resistance in terms of current and voltage. Then solve the following: A certain device in a 120 V circuit has a current rating of 30 A. What is the resistance of the device (how many ohms)?

12) A 7 W night light is plugged into a 120 V circuit and operates continuously for 1 year. Find the following:

(a) the current it draws

(b) the resistance of its filament

(c) the energy consumed in a year

(d) the cost of its operation for a year at the utility rate of $0.08/kWh

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