Transcript Powerpoint Slides

Lab 3: Series & Parallel Resistors
Only 9 more labs to go!!
The energy can be extracted from the water if we
let it fall over a waterwheel.
water flow
h 
electric potential, V
m
charge, q
water flow  current, I
potential energy, mgh  qV
water wheel  resistor
PE = mgh
If we have more than one resistor
(or waterwheel) then we have a
couple of choices as to how to connect
them to the power source
R, resistor
Potential V
Current, 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)
water flow
V1
I
I
htotal
h2
V2
VTotal
h1
R1
R2
I
• The total resistance
of the circuit, as felt by
the battery will be the
sum of all individual
resistances
RTotal = R1 + R2
We could connect them in Parallel
ITotal
I1
I2
V
V
R1
I1
h
V
R2
I2
ITotal
• 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
1
RTotal

1
1

R1 R2
Circuit analysis, you will be asked to do circuit analysis on the quiz.
Consider the following circuit:
R1 = 50 
R2 = 75 
R3 = 25 
V = 10 V
R4 = 10 
Let’s find the voltage drop across each resistor. The 1st step is to
reduce the circuit to an equivalent resistance.
V = 10 V
R12 = 125 
R12 = R1 + R2 = 50 + 75
R34 = 7.1 
1
1
1
1
1
14





R34 R3 R4 25 10 100
Take one over! DON’T FORGET!
IT = 0.076 A
V = 10 V
R1234 = 132.1 
R1234 = R12 + R34 = 125 + 7.1 
Using Ohm’s law we can calculate the current
through the circuit:
V
10V
IT  
 0.076 A
R 132.1
Next we can calculate the voltage drop across the two equivalent resistors, R12 and R34
IT = 0.076 A
V = 10 V
R12 = 125  V12 = 9.5 V
V12 = IT R12 = (0.076 A) (125 ) = 9.5 V
R34 = 7.1  V34 = 0.54 V
V34= IT R34= (0.076 A) (7.1 ) = 0.54 V
Finally we can find the voltage dropped across each resistor
V1 = IT R1 = (0.076 A)(50 ) = 3.8 V
R1 = 50 
V2 = IT R2 = (0.076 A)(75 ) = 5.7 V
R2 = 75  V2 = 5.7 V
IT = 0.076 A
V1 = 3.8 V
R3 = 25 
V3 = 0.54 V
V = 10 V
R4 = 10 
V4 = 0.54 V
How could we measure the voltages and currents?
We need to use Voltmeters (connected in parallel) for the voltage
and Ampmeters (connected in series) to measure the current
Measuring current
through R1 and R2
R1 = 50 
R2 = 75 
Amp
Series
V = 10 V
R3 = 25 
Amp
Series
R4 = 10 
Volts
Parallel
Measuring the voltage
across R3 and R4
Measuring current
through R3
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 indicates
the 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
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
4th Stripe
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)