CST1511Basic Electricity - 2

Extra Credit Lecture

Gary C. Meyer, Instructor

Review of Ohms Law/Power Formulas

E = IRI = E/RR = E/I

P = EIP = I2RP = E2/R

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

R (Total) =

_______

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

R (Total) =

_ 30 ohms __

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

I (Total) =

+ 30 V -

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

I (Total) = E/R = 30/30 = 1 A

+ 30 V -

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

V (R2) = _____________

+ 30 V -

Series Resistors R(Total) = R1 +R2 + R3Example:

R1 = 15Ω R2 = 10Ω R3 = 5Ω

V (R2) = I x R = 1 x 10 = 10 v

+ 30 V -

Current in Series CircuitUse Ohm’s LawExample:

R1 = 8k ohm

I(R1) =

R2 = 2k ohm

E = 10 volts

I (R1) = ?

Current in Series CircuitUse Ohm’s LawExample:

R1 = 8k ohm

IR1 = 10/(8000 + 2000) = 0.001 Amps

R2 = 2k ohm

E = 10 volts

I R1 = ?

Voltage in Series CircuitVoltage Divides Across ResistorsExample: First Find Current. Next find

voltages.

R1 = 1k ohm

I =

R2 = 2k ohm

E = 100 volts

V1 = I1 x R1

V2 = I2 x R2

V1 =

V2 =

Voltage in Series CircuitVoltage Divides Across ResistorsExample: First Find Current. Next find

voltages.

R1 = 1k ohm

I = 100/(1000 + 2000) = 0.0333 Amps R2 = 2k

ohm

E = 100 volts

V1 = I1 x R1

V2 = I2 x R2

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

R (Total) =

R2 = 50

Parallel Resistors (For Two)R(Total) = (R1 x R2)/(R1 + R2)Example: Rt = ?

R1 = 100

R (Total) =

(100 x 50)/150 = 33.33Ω

R2 = 50

Parallel Resistors (For Two)R(Total) = (R1 x R2)/(R1 + R2)Example: Rt = ?

R1 = 2 kohms

R (Total) = ?

R2 = 3 kohms

Parallel Resistors (For Two)R(Total) = (R1 x R2)/(R1 + R2)Example: Rt = ?

R1 = 2 kohms

R (Total) =

(2000 x 3000)/5000 = 1200 Ω

R2 = 3 kohms

Current In Parallel CircuitUse Ohm’s LawExample: I1 =

I2= R1 = 25

E = 100 v

E/R1 = 100/25 = 4 A

R2 = 50

E/R2 = 100/50 = 2 A

I1 + I2 = 6 AmpsIt =

Power In Parallel CircuitUse Power FormulasExample: P1 =

P2= R1 = 25

E = 100 v

E x I = 100 x 4 = 400 watts

R2 = 50

E x I = 100 x 2 = 200 watts

P1 + P2 = 600 watts

Pt =

Parallel Resistors1/R(Total) = 1/R1 + 1/R2 + 1/R3Example:

1/Rt = 1/3 + 1/5 + 1/10 = .33 + .20 + 0.10 = 0.63 Ω R1 =

3Ω

R (Total) = 1/0.63 = 1.59 ohms

R2 = 5Ω

R3 = 10Ω

Parallel Resistors1/R(Total) = 1/R1 + 1/R2 + 1/R3Problem

R1 = 2 kΩ

R (Total) = ______________

R2 = 500Ω

R3 = 10Ω

Parallel Resistors1/R(Total) = 1/R1 + 1/R2 + 1/R3Problem

R1 = 2 kΩ

R (Total) = 9.75 ohms

R2 = 500Ω

R3 = 10Ω

1/R (total) = 1/2000 + 1/500 +1/10

1/R (Total)= .0005 + .002 + .1

1/R (Total) = .1025

R (Total) = 1/0.1025

Parallel Resistors1/R(Total) = 1/R1 + 1/R2 + 1/R3Problem I = E/R

R1 = 2 kΩ

R2 = 500Ω

R3 = 10Ω

12 v

Solve for all currents.

I (R1) =

I (R2) =

I (R3) =

I (total) =

Parallel Resistors1/R(Total) = 1/R1 + 1/R2 + 1/R3Problem I = E/R

R1 = 2 kΩ

R2 = 500Ω

R3 = 10Ω

12 v

Solve for all currents.

I (R1) = 12/2000 = .006 A

I (R2) = 12/500 = .024 A

I (R3) = 12 /10 = 1.2 A

I (total) = 1.230 A

Series/Parallel ResistorsUse Same PrinciplesExample:

R1 = 100

R (Total) =

100 + (50x50)/(50+50) + 60 = 185Ω

R2 = 50

R3 = 50

R4 = 60

Currents in Combined CircuitUse Resistance Rules + Ohm’s Law

Example: Rt = 185 ohms from a previous example.R1 = 100

I (Total) =E/R = 370/185 = 2 A

R2 = 50

R3 = 50

R4 = 60

E = 370 v

IR2 = ? IR3 =?

IR2 = IR3 = 1 A

Equal resistors = Equal currents

Voltages in Combined CircuitUse Resistance Rules + Ohm’s Law

Example: Rt = 185 ohms from previous example.R1 = 100

I (Total) =E/R = 370/185 = 2 A

R2 = 50

R3 = 50

R4 = 60

E = 370 v

VR1 =IR1 x R1 = 2 x 100 = 200 v

Voltages in Combined CircuitUse Resistance Rules + Ohm’s Law

Example: Rt = 185 ohms from previous example.R1 = 100

I (Total) =E/R = 370/185 = 2 A

R2 = 50

R3 = 50

R4 = 60

E = 370 v

VR2 =IR2 x R2 = 1 x 50 = 50 v

Voltages in Combined CircuitUse Resistance Rules + Ohm’s Law

Example: Rt = 185 ohms from previous example.R1 = 100

I (Total) =E/R = 370/185 = 2 A

R2 = 50

R3 = 50

R4 = 60

E = 370 v

VR4 =IR3 x R3 = 2 x 60 = 120 v

Parallel Resistor CurrentsExample ProblemExample: What is the current in the 20 ohm resistor?

R1 = 100

R2 =20

R3 = 40

R4 = 100

It = 0.6 AIR2 = R3/(R2 + R3) x (It) = 40/60 x .6 = 0.4 AIR3 = R2/(R2 + R3) x (It) = 20/60 x .6 = 0.2 A

IR2

IR3

Parallel Resistor CurrentsProblemExample: What is the current in the 20 ohm resistor?

R1 = 50

R2 =10

R3 = 10

R4 = 20

It = 1.0 AIR2 = R3/(R2 + R3) x (It) =

IR3 = R2/(R2 + R3) x (It) =

IR2

IR3

Parallel/Series Resistor VoltagesProblemExample: What is the current in the 20 ohm resistor?

R1 = 50

R2 =10

R3 = 10

R4 = 20

It = 1.0 AV (R1) =

V (R2) =

IR2

IR3

V (R4) =

V (Total) =

Parallel/Series Resistor VoltagesSolutionExample: What is the current in the 20 ohm resistor?

R1 = 50

R2 =10

R3 = 10

R4 = 20

It = 1.0 AV (R1) = 1 x 50 = 50v

V (R2) = 0.5 x 10 = 5 v

IR2

IR3

V (R4) = 1 x 20 = 20 v

V (Total) = 50 + 5 + 20 = 75 v

Complete Worksheet 10Basic Electricity - 2Optional – Extra Credit

JPG FilePlace Worksheet in Dropbox

for Worksheet 10