NOW, moving on to circuits…

Four devices are commonly used in the laboratory to study Ohm’s law: the battery, the voltmeter, the ammeter and a resistance. The ammeter and voltmeter measure current and voltage respectively.

Ammeter measures current through the battery, the filament,

and itself.

This arrangement measuresthe voltage across the battery.

The following symbols are used in electric circuits:

Reading a resistor code.

RESISTORS IN SERIES

To wire in SERIES means to make a circuit with a single pathway for the current.

RULES FOR RESISTORS IN SERIES

- In a series circuit, the current is the same at all points along the wire.  IT = I1 = I2 = I3

 - An equivalent resistance is the resistance of a single resistor that could replace all the resistors in a circuit. The single resistor would have the same current through it as the resistors it replaced.  RE= R1 + R2 + R3

 - In a series circuit, the sum of the voltage drops equal the voltage drop across the entire circuit.

VT = V1 + V2 + V3

Example: Two resistances of 2 Ω and 4 Ω respectively are connected in series. If the source of emf maintains a constant potential difference of 12 V,a. What is the current delivered to the external circuit?

Re = R1 + R2

= 2 + 4 = 6 Ω

IV

RTe

12

6= 2 A

b. What is the potential drop across each resistor?

V1 = I R1

= 2(2) = 4 VV2 = I R2

= 2(4) = 8 V

RESISTORS IN PARALLEL

To wire in PARALLEL means to make a circuit with multiple pathways for the current.

PARALLEL CIRCUITS

- In a parallel circuit, each resistor provides a new path for electrons to flow. The total current is the sum of the currents through each resistor.  IT = I1 + I2 + I3

- The equivalent resistance of a parallel circuit decreases as each new resistor is added.  

- The voltage drop across each branch is equal to the voltage of the source.

VT = V1 = V2 = V3

1 1 1 1

1 2 3R R R RE

Example: A 5Ω and 10Ω resistor are wired in parallel to 6V battery. A. What is their equivalent resistance?

R1= 5ΩR2 = 10ΩV= 6V

1 = 1 + 1RT 5 10

RT = 3.33 Ω

B. What is the current through each resistor?

IV

R = 6 V

5 Ω= 1.2 A

= 6 V 10 Ω

= 0.6 AIV

R

IV

R = 6 V

3.33Ω

IT= 1.80AIT= 1.80A

No examples in the PSE, the notes will not be online, you may want to . . .

fetch some paper… and a calculator…

Why can a bird stand on a high voltage wire and not get shocked?

Because there is no Potential difference between his feet.

Will either bird get shocked now?

Yes, the one over the light bulb, because a potential difference exists between his feet.

A word about Electrical Safety…Ground plugs. One end of the ground plug is connected to the appliance cover. The wall jack which receives the ground plug is connected to the ground, so any charge leaking onto the appliance will drain to ground not you.

If not…

You are the path of least resistance..

One milliampere: tingling sensationTen milliamperes: nerves and muscles overloaded200 milliamperes: potentially fatal; heart fibrillation500 -1000 milliamperes: not necessarily fatal; heart will restartOne ampere or more: burn alive

As more and more appliances are added to a circuit in parallel the resistance decreases and the current increases. Too much current can result in an overload and a possible fire.

Fuses and Circuit breakers are used to prevent overload, by limiting the amount of current that can flow through a circuit.

A fuse uses a thin metal wire or ribbon that melts when current through it is too high. These must be replaced.

Brass expands more than steel As temperature increases, the bimetallic strip arcs to the left,settles into groove, and the spring pulls the metal bar down breaking the circuit.

Houses today use CIRCUIT BREAKERS. These do not need to be replaced and use a bimetallic strip that trips a switch.

We will use Equivalent Resistance …

How can we solve complex circuits?That is circuits that have both parallel and series components?

Equivalent Resistance simplifies a circuit by replacing resistor sets with a single EQUAL resistor…

For example:

The 8Ω and 4Ω resistors are in series so could be replaced with a 12Ω resistor

The 6Ω and 3Ω resistors are in parallel. They can be replaced with a single 2 Ω resistor.The 12 Ω and 2 Ω resistors are in series and could be replaced with a single 14 Ω resistor.

Example: The total applied voltage to the circuit in the figure is 12 V and the resistances R1, R2 and R3 are 4, 3 and 6 Ω respectively.a. Determine the equivalent resistance of the circuit.

R2 and R3 are in parallel (RP)

1 1

6

1

3Rp Rp= 2 Ω

RP and R1 are in series

Req = 4 + 2 = 6 Ω

The total applied voltage to the circuit in the figure is 12 V and the resistances R1, R2 and R3 are 4, 3 and 6 Ω respectively. (b) What is the total current?

I = V/R 12V/6Ω =2 A

(c) Find the current through and the voltage across each resistor.

R1: I = 2 A (series) soV=IR= (2 A)(4 Ω) = 8V

The remaining voltage in the circuit is 12 V – 8 V = 4 Vwhich means that V2 and V3 are 4 V since they are

in parallel.I = V/R

I2 = 4V / 3Ω =

1.33 A

I3 = 4V / 6Ω =0.67 A