Chapter 18EMF

Parallel CircuitsSeries Circuits

So, when the electric company sends you a bill at the end ofthe month, what are they charging you for?

Well, what are the units of the quantity for which they bill you?

Kilowatt-Hours

103 W - Hours103 (J/s) Hours

103 (J/s) Hours (3600 s/Hour)3.6 X 106 J

We’ve looked at simple series and parallelcircuits involving batteries and capacitors.We now examine series and parallel circuitsinvolving batteries and resistors. We’ll confineour comments in this chapter to “directcurrent” circuits – that is, circuits in which thecurrent flows in only one direction.

DC Circuits

The “electromotive force”

The term “electromotive force” has fallen out offavor since it really is not a force at all!However, the term “EMF” has stuck and is usedin the description of devices which increasethe potential energy of charges flowing in acircuit. Such devices are called sources of emf.

You’ve probably noticed by now that wephysicists use the letter “E” an awful lot…There’s energy and electric fields, besidesthe e representing the exponential function...

Well, guess what letter is used to representthe new quantity “emf?”

So, in an attempt tominimize your confusionover the different E’s, Iwill use the followingnotation...

E represents Energy

E represents the Electric Field

And represents the EMF.

Watch out!This is slightly different than the book!

+ _ For the case of a batterywith no internal resistance

= V

The EMF and the potential are closely related. In fact, they have the same units: Volts.

Of course, real batteries have some internalresistance, such that

V R

Rint

I

V = - I Rint

load resistor

internal resistance

terminal voltage

V R

Rint

I

What is thecurrent in thiscircuit?

= I Rint + I R

I = Rint + R

What is the powersupplied by the EMF?

What is the power supplied by the battery?

P = I V = I2 R

So what happenedto the difference?

P = I = I2 (Rint + R)

The lost power in the battery (or resistor) that goes into heating it. Check out the temperature of rechargeable batteries next time you use them...

“Joule Heating”

For MOST cases we will deal with Rint << R

so we usually neglect Rint

Unless otherwise stated Rint = 0!

But many other devices are designed to take advantage of Joule heating. Perhaps you can think of a few?

Joule heating in a battery is not desirable -- it’s power lost in the battery that cannot be used by the other devices in the circuit.

So, what happens after the battery is connected to this circuit?

V1 + V2 = V

I1 = I2 due to conservation of charge!

V R2

+

_R1

I1

I2

We can construct an equivalent circuit with a single resistor...

V = V1 + V2 = I R1 + I R2 = I (R1 + R2)

V R2

+

_R1

I

I

V = I Req

V Req

+

_I

Req = R1 + R2

Resistors in series ADD.

V Req

+

_

V = V1 + V2 = I R1 + I R2 = I (R1 + R2)

V = I Req

What happens ina series circuit ifone of the resistorsburns out?

V R2

+

_R1

I

I = 0

When one element fails, the circuit is broken;the current ceases to flow; and all the otherelements (in the same branch of the circuit) stop functioning as well.

Old Christmas tree lights used to be wired inseries. When one bulb burned out, the wholestring of lights went dark. Figuring out whichbulb had failed could be quite a chore!

Is there any time you might want to use aseries circuit?

Well, a fuse box or circuit breaker box is a goodplace to use a series circuit.

When the appliances in your house draw toomuch current, a potential fire hazard exists.

(Too much current leads to too much joule heating of the wires.)

Circuit breakers and fuses are designed tofail when the currents through them becometoo large.

By sending power into your house through acircuit breaker or fuse, you prevent large currents from entering the house.

The circuit breaker (fuse) is wired in series with the electrical outlets in the house. The outlets are actually wired in parallel with each other.

BreakerBox

Outlets with Appliances

I

When the breaker is tripped, current ceases toflow to the outlets connected to that circuit in the house.

BreakerBox

Outlets with Appliances

No Current!

So, what happens after the battery is connected to this circuit?

The current divides, with part of it going through R1 and part of it going through R2.

V R2

+

_R1

The voltage across R1 and R2 must be the same!

I

I1

I2

Just like capacitors in parallel!