### CST1511_BasicElectricity_2

```Extra Credit Lecture
Gary C. Meyer, Instructor
Review of Ohms Law/Power Formulas
 E = IR
 I = E/R
 R = E/I
 P = EI
 P = I2R
 P = E2/R
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
R (Total) =
_______
R3 = 5Ω
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
R (Total) =
R3 = 5Ω
_ 30 ohms __
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
+ 30 V I (Total) =
R3 = 5Ω
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
R3 = 5Ω
+ 30 V I (Total) = E/R = 30/30 = 1 A
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
+ 30 V V (R2) = _____________
R3 = 5Ω
Series Resistors
 R(Total) = R1 +R2 + R3
 Example:
R1 = 15Ω
R2 = 10Ω
R3 = 5Ω
+ 30 V V (R2) = I x R = 1 x 10 = 10 v
Current in Series Circuit
 Use Ohm’s Law
 Example:
R1 = 8k ohm
R2 = 2k ohm
I (R1) = ?
E = 10 volts
I(R1) =
Current in Series Circuit
 Use Ohm’s Law
 Example:
R1 = 8k ohm
R2 = 2k ohm
I R1 = ?
E = 10 volts
IR1 =
10/(8000 + 2000) = 0.001 Amps
Voltage in Series Circuit
 Voltage Divides Across Resistors
 Example: First Find Current. Next find voltages.
I=
R1 = 1k ohm
V1 = I1 x R1
R2 = 2k ohm
V2 = I2 x R2
E = 100 volts
V1 =
V2 =
Voltage in Series Circuit
 Voltage Divides Across Resistors
 Example: First Find Current. Next find voltages.
I=
100/(1000 + 2000) = 0.0333 Amps
R1 = 1k ohm
R2 = 2k ohm
V1 = I1 x R1
V2 = I2 x R2
E = 100 volts
V1 = 0.0333 x 1000 = 33.3 v
V2 = 0.0333 x 2000 = 66.6 v
Parallel Resistors (For Two)
 R(Total) = (R1 x R2)/(R1 + R2)
 Example: Rt = ?
R1 = 100
R2 = 50
R (Total) =
Parallel Resistors (For Two)
 R(Total) = (R1 x R2)/(R1 + R2)
 Example: Rt = ?
R1 = 100
R2 = 50
R (Total) =
(100 x 50)/150 = 33.33Ω
Parallel Resistors (For Two)
 R(Total) = (R1 x R2)/(R1 + R2)
 Example: Rt = ?
R1 = 2 kohms
R2 = 3 kohms
R (Total) = ?
Parallel Resistors (For Two)
 R(Total) = (R1 x R2)/(R1 + R2)
 Example: Rt = ?
R1 = 2 kohms
R2 = 3 kohms
R (Total) =
(2000 x 3000)/5000 = 1200 Ω
Current In Parallel Circuit
 Use Ohm’s Law
 Example: I1 = E/R1 = 100/25 = 4 A
I2= E/R2 = 100/50 = 2 A
R1 = 25
R2 = 50
E = 100 v
It = I1 + I2 = 6 Amps
Power In Parallel Circuit
 Use Power Formulas
 Example: P1 = E x I = 100 x 4 = 400 watts
P2= E x I = 100 x 2 = 200 watts
R1 = 25
R2 = 50
E = 100 v
Pt = P1 + P2 = 600 watts
Parallel Resistors
 1/R(Total) = 1/R1 + 1/R2 + 1/R3
 Example:
1/Rt = 1/3 + 1/5 + 1/10 = .33 + .20 + 0.10 = 0.63 Ω
R1 = 3Ω
R2 = 5Ω
R3 = 10Ω
R (Total) = 1/0.63 = 1.59 ohms
Parallel Resistors
 1/R(Total) = 1/R1 + 1/R2 + 1/R3
 Problem
R1 = 2 kΩ
R2 = 500Ω
R3 = 10Ω
R (Total) = ______________
Parallel Resistors
 1/R(Total) = 1/R1 + 1/R2 + 1/R3
 Problem
R1 = 2 kΩ
1/R (total) = 1/2000 + 1/500 +1/10
1/R (Total)= .0005 + .002 + .1
R2 = 500Ω
1/R (Total) = .1025
R (Total) = 1/0.1025
R3 = 10Ω
R (Total) = 9.75 ohms
Parallel Resistors
 1/R(Total) = 1/R1 + 1/R2 + 1/R3
 Problem
I = E/R
Solve for all currents.
R1 = 2 kΩ
I (R1) =
I (R2) =
R2 = 500Ω
I (R3) =
I (total) =
R3 = 10Ω
12 v
Parallel Resistors
 1/R(Total) = 1/R1 + 1/R2 + 1/R3
 Problem
I = E/R
Solve for all currents.
R1 = 2 kΩ
R2 = 500Ω
I (R1) = 12/2000 = .006 A
I (R2) = 12/500 = .024 A
I (R3) = 12 /10 = 1.2 A
R3 = 10Ω
I (total) = 1.230 A
12 v
Series/Parallel Resistors
 Use Same Principles
 Example:
R2 = 50
R1 = 100
R4 = 60
R3 = 50
R (Total) =
100 + (50x50)/(50+50) + 60 = 185Ω
Currents in Combined Circuit
 Use Resistance Rules + Ohm’s Law
 Example: Rt = 185 ohms from a previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
Equal resistors =
Equal currents
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
IR2 = ? IR3 =? IR2 = IR3 = 1 A
Voltages in Combined Circuit
 Use Resistance Rules + Ohm’s Law
 Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR1 = IR1 x R1 = 2 x 100 = 200 v
Voltages in Combined Circuit
 Use Resistance Rules + Ohm’s Law
 Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR2 = IR2 x R2 = 1 x 50 = 50 v
Voltages in Combined Circuit
 Use Resistance Rules + Ohm’s Law
 Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR4 = IR3 x R3 = 2 x 60 = 120 v
Parallel Resistor Currents
 Example Problem
 Example: What is the current in the 20 ohm resistor?
R2 =20
R1 = 100
R4 = 100
IR2
R3 = 40
It =
0.6 A
IR3
IR2 = R3/(R2 + R3) x (It) = 40/60 x .6 = 0.4 A
IR3 = R2/(R2 + R3) x (It) = 20/60 x .6 = 0.2 A
Parallel Resistor Currents
 Problem
 Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
IR2 = R3/(R2 + R3) x (It) =
IR3 = R2/(R2 + R3) x (It) =
Parallel/Series Resistor Voltages
 Problem
 Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
V (R1) =
V (R2) =
V (R4) =
V (Total) =
Parallel/Series Resistor Voltages
 Solution
 Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
V (R1) = 1 x 50 = 50v
V (R2) = 0.5 x 10 = 5 v
V (R4) = 1 x 20 = 20 v
V (Total) = 50 + 5 + 20 = 75 v
Optional – Extra Credit
JPG File
Place Worksheet in Dropbox
for Worksheet 10
```