Presentation: advanced electricity

Gum wrapper (foil-covered paper), cut into a strip, with a narrow center section: check. AA battery: check. Completing an electrical circuit to start a fire: priceless. (Video link: "How to Make A Prison Lighter From a Bubble Gum Wrapper. MUST SEE! :)")

In this presentation we introduce a few additional concepts as we further implement Kirchhoff's circuit rules in analyzing electrical circuits.

The videos shown in this presentation, as with many videos shown in this class, should never be attempted at home. Even if many of these videos use items commonly found at home. Even if these items are found, well, within the very walls of your house itself!

First, using the digital multimeters used in laboratory to measure current, or to measure voltage.

You have already used these digital multimeters to measure the resistance of Christmas light bulbs, when isolated from an electrical circuit, when the proper plugs and correct dial settings are used. These digital multimeters can also measure current or electric potential rises/drops of items wired in an active electrical circuit, provided the proper plugs and correct dial settings are used. And since measurements are being made on an item while the circuit is "live," some care must be taken in not only using the proper plugs and correct dial settings, but also in properly connecting the digital multimeter to the item of interest.

When measuring the current passing through a light bulb (or any other circuit element), the current that passes through the light bulb must also pass through the digital multimeter. This means that the wiring in the circuit must be "broken" open to connect the digital multimeter to measure current (making it an ammeter).

Does it matter whether the ammeter is connected to measure current before it passes through the light bulb, or to measure current after it passes through the light bulb?

Why must an ammeter have a resistance that is ideally zero (or at the very least, a very low resistance value)?

When measuring the amount of electrical potential used by a light bulb (or any other circuit element), the digital multimeter must be connected to both before and the current flows through the light bulb. This means that the wiring in the circuit is not modified in order to connect the digital multimeter to measure electric potential (making it an voltmeter), as it "feels" the amount of electric potential before and after the light bulb, and reports the difference (whether a drop or rise).

Why must a voltmeter have a resistance that is ideally infinity (or at the very least, a very high resistance value)?

Second, the rate of energy per time (power) used by a circuit element.

"Joule heating" is the historical term for the power (or rate of energy used per time) continuously used by a circuit element of resistance R due to the amount of current I flowing through it, as in these radiating coils.

(For the purposes of this class, we will consider the resistance R of materials to be constant with respect to temperature, although the resistivity of many materials will typically be strongly dependent on the temperature.)

Recall from a previous presentation that a change in electric potential ∆V represents the "potential" potential energy used by a charge. For each charge q that uses a certain amount ∆V of electric potential, the amount of electric potential energy used is ∆EPE = q·∆V. For a continuous flow of charges per time as in a current I, the rate of electric potential energy used per time (that is, power) is ∆EPE/∆t = (q·∆V)/∆t = (q/∆t)·∆V = I·∆V.

(If instead the ∆V represents a rise in electric potential (as in a battery) instead of a drop, then I·∆V represents the continuous rate of electric potential energy per time provided by the battery.)

Substituting in Ohm's law (I = ∆V/R), the two parameters I and ∆V in the power equation can each be substituted out, yielding two other equivalent equations for power, most notoriously, the "Twinkle, Twinkle, Little Star" form:

Twinkle, twinkle, little star
Power equals I-squared R.

Believe me, you won't get this out of your head. Ever.

So endless hours of amusement await you when solving power dissipation (or source) problems, so use caution when you use these equations, and more importantly, use only the equation you really need.

All household electrical outlets provide 120 volts of electric potential and operate independently of each other, and thus are wired in parallel to each other to the same 120 volt electromotive source. Recall that from a previous presentation that as more resistors are added in parallel to a circuit, the equivalent resistance decreases. This means that as more and more appliances are plugged into the same household circuit and turned on, then the equivalent resistance may become dangerously low.

This may result in a very large runaway current flowing through the wires leading to the overloaded outlets. Even though the wires ideally have a low resistance r, a large enough current I will cause the wire to heat up appreciably (as the rate of joule heating is I²·r), resulting in the insulation around the wires, and the joists and walls in contact with it to catch on fire.

In order to prevent runaway currents from happening in a household circuit (well, should common sense fail to prevent overuse of the outlets), a circuit breaker is designed to "trip" and interrupt the current should it become dangerously high. If this should happen, protocol is to first unplug any and all appliances in that part of your house before resetting the breaker to re-complete the circuit. (Video link: "A 6 Amp AC breaker trips on DC at 240 Volts 30 Amps.")

Remember the gum wrapper and AA battery fire starter at the start of this presentation? That is an analog for an older-type fuse that would have a slightly greater resistance than the wires, such that the fuse would experience higher joule heating and sacrificially melt first before the wires would themselves heat up, breaking the circuit. Unlike modern circuit breakers, a fuse is no longer functional after melting, and must be completely replaced. A highly dangerous, but unfortunately common workaround for when a replacement fuse was not readily available was to push a penny (or other small piece of conducting metal) into the fuse socket in order to re-complete the circuit--hopefully after unplugging any and all appliances in that part of the house!