Lab 3: Series & Parallel ResistorsOnly 9 more labs to go!!

Potential VR, resistor

Current, I

water flow

The energy can be extracted from the water if welet it fall over a waterwheel.

PE = mgh

h electric potential, Vm charge, qwater flow current, Ipotential energy, mgh qVwater wheel resistor

If we have more than one resistor(or waterwheel) then we have a couple of choices as to how to connectthem to the power source

htotal

water flow

h1

h2

I

I

We could connect them in series

• The current through each wheel (resistor) is the same• The height drop (potential energy, voltage) across each wheel (resistor) will add to the total height (total voltage)

VTotal

R1

I

R2

• The total resistanceof the circuit, as felt bythe battery will be thesum of all individual resistances

RTotal = R1 + R2

V1

V2

h

ITotal I1

I2

We could connect them in Parallel

V

ITotal

I1 I2

R1 R2

V V

• The current that flows through each resistor will add up to the total delivered by the power source

• The electric potential (voltage) will be the same across each resistor

• The total resistance seen by the power supply will always be less than any individual resistor

21

111

RRRTotal

Circuit analysis, you will be asked to do circuit analysis on the quiz.Consider the following circuit:

V = 10 V

R1 = 50 R2 = 75

R3 = 25

R4 = 10

Let’s find the voltage drop across each resistor. The 1st step is toreduce the circuit to an equivalent resistance.

V = 10 V

R12 = 125

R34 = 7.1

R12 = R1 + R2 = 50 + 75

100

14

10

1

25

1111

4334 RRR

V = 10 V

R1234 = 132.1 R1234 = R12 + R34 = 125 + 7.1

Using Ohm’s law we can calculate the currentthrough the circuit:

AV

R

VIT 076.0

1.132

10

IT = 0.076 A

Next we can calculate the voltage drop across the two equivalent resistors, R12 and R34

V = 10 V

R12 = 125 V12 = 9.5 V

R34 = 7.1 V34 = 0.54 V

IT = 0.076 A V12 = IT R12 = (0.076 A) (125 ) = 9.5 V

V34= IT R34= (0.076 A) (7.1 ) = 0.54 V

Take one over! DON’T FORGET!

V = 10 V

R1 = 50 R2 = 75 V2 = 5.7 V

R3 = 25 V3 = 0.54 V

R4 = 10 V4 = 0.54 V

Finally we can find the voltage dropped across each resistor

IT = 0.076 A

V1 = IT R1 = (0.076 A)(50 ) = 3.8 V

V1 = 3.8 V

V2 = IT R2 = (0.076 A)(75 ) = 5.7 V

How could we measure the voltages and currents?

We need to use Voltmeters (connected in parallel) for the voltageand Ampmeters (connected in series) to measure the current

V = 10 V

R1 = 50 R2 = 75

R3 = 25

R4 = 10

AmpSeries

VoltsParallel

AmpSeries

Measuring currentthrough R1 and R2

Measuring currentthrough R3

Measuring the voltageacross R3 and R4

To calculate the value of a resistor using the color coded stripes on the resistor,use the following procedure.

Step One: Turn the resistor so that the gold or silver stripe is at the right end of the resistor.

Step Two: Look at the color of the first two stripes on the left end. These correspond to the first two digits of the resistor value. Use the table given below to determine the first two digits.

Step Three: Look at the third stripe from the left. This corresponds to a multiplication value. Find the value using the table below.

Step Four: Multiply the two digit number from step two by the number from step three.This is the value of the resistor n ohms. The fourth stripe indicatesthe accuracy of the resistor. A gold stripe means the value of the resistor may vary by 5% from the value given by the stripes.

Color 1st Stripe 2nd Stripe 3rd Stripe 4th Stripe

Black 0 0 x1

Brown 1 1 x10

Red 2 2 x100

Orange 3 3 x1,000

Yellow 4 4 x10,000

Green 5 5 x100,000

Blue 6 6 x1,000,000

Purple 7 7

Gray 8 8

White 9 9

Gold 5%

Silver 10%

Example1: You are given a resistor whose stripes are colored from left to right as brown, black, orange, gold. Find the resistance value. Step One: The gold stripe is on the right so go to Step Two. Step Two: The first stripe is brown which has a value of 1. The second stripe is black which has a value of 0. Therefore the first two digits of the resistance value are 10. Step Three: The third stripe is orange which means x 1,000. Step Four: The value of the resistance is found as 10 x 1000 = 10,000 ohms (10 kilohms = 10 kohms). The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be somewhere between 9,500 ohms and 10,500 ohms. (Since 5% of 10,000 = 0.05 x 10,000 = 500)   Example2: You are given a resistor whose stripes are colored from left to right as orange, orange, brown, silver. Find the resistance value. Step One: The silver stripe is on the right so go to Step Two. Step Two: The first stripe is orange which has a value of 3. The second stripe is orange which has a value of 3. Therefore the first two digits of the resistance value are 33. Step Three: The third stripe is brown which means x 10. Step Four: The value of the resistance is found as 33 x 10 = 330 ohms. The silver stripe means the actual value of the resistor mar vary by 10% meaning the actual value will be between 297 ohms and 363 ohms. (Since 10% of 330 = 0.10 x 330 = 33)   Example3: You are given a resistor whose stripes are colored from left to right as blue, gray, red, gold. Find the resistance value. Step One: The gold stripe is on the right so go to Step Two. Step Two: The first stripe is blue which has a value of 6. The second stripe is gray which has a value of 8. Therefore the first two digits of the resistance value are 68. Step Three: The third stripe is red which means x 100. Step Four: The value of the resistance is found as 68 x 100 = 6800 ohms (6.8 kilohms = 6.8 kohms). The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be somewhere between 6,460 ohms and 7,140 ohms. (Since 5% of 6,800 = 0.05 x 6,800 = 340)   Example 4: You are given a resistor whose stripes are colored from left to right as green, brown, black, gold. Find the resistance value. Step One: The gold stripe is on the right so go to Step Two. Step Two: The first stripe is green which has a value of 5. The second stripe is brown which has a value of 1. Therefore the first two digits of the resistance value are 51. Step Three: The third stripe is black which means x 1. Step Four: The value of the resistance is found as 51 x 1 = 51 ohms. The gold stripe means the actual value of the resistor mar vary by 5% meaning the actual value will be somewhere between 48.45 ohms and 53.55 ohms. (Since 5% of 51 = 0.05 x 51 = 2.55)