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Lecture 5 - Basic Resistive Electrical Circuits

Series Circuits

Parallel Circuits

Combinational Circuits

Maximum Power Transfer

AC Voltage and Current – Time Domain Waveforms

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Lecture 5 - Basic Resistive Circuits

Basic DC Electric Circuits Examples (source: http://hyperphysics.phy-

astr.gsu.edu/hbase/electric/dcex.html)

Multisim Circuit Simulation

DC Circuit Construction, PhET Interactive Simulations,

http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc2

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Series Circuits

Two Resistors R1, R2 in series

DC power source

Rt = R1 + R2

It = Edc/Rt

Conventional current flow

direction

I1 = I2 = It

V1 = I1* R1

V2 = I2 * R2

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R1

100ΩR2

200ΩEdc

24 V

S1F1 R1

100ΩR2

200ΩEdc

24 V

S1F1

Power Calculation

P1 = V1*I1

P2 = V2 * I2

Pt = Edc * It

Series Circuits (cont.)

N Light Bulbs in series

AC power source

One LB failed, the circuit is not

functional

Rt = R1 + R2 + … + Rn

It = E/Rt

Conventional current flow

direction

It = I1 = I2 = In

E = V1 + V2 + … + Vn

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Power Calculation

P1 = V1*I1

P2 = V2 * I2

Pn = Vn * In

Pt = E * It

E

F1S1

LB1 LB2

LBn

120V rms

Christmas Tree Lighting System

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Parallel Circuits

Two Resistors R1, R2 in Parall

DC power source

Rt = R1 || R2 = (R1*R2)/(R1+R2)

It = Edc/Rt

Conventional current flow direction

V1 = V2 = Edc

I1 = V1 ÷ R1 = V1 / R1

I2 = V2 / R2

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Power Calculation

P1 = V1 * I1

P2 = V2 * I2

Pt = Edc * It

R1

100Ω

R2

200ΩEdc

24 V

S1F1

Parallel Circuits (continue)

Three Light Bulbs in Parallel

AC 120V power source

P = I2*R = E2/R

E = V1 = V2 = V3

I1 = I2 = I3 = P/E = 100w/120v =

0.83A

It = I1 + I2 + I3 = 2.49 A

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E

F1S1

LB1 LB2 LB3

120V 100W x 3

120V rms

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Series Circuit Calculations

• What is the total resistance Rt?

• Rt = 900 Ω = ______________________

• What is I1, I2, I3, and It?

• It = Et/Rt = 111.11 mA

• Voltage drops: V1, V2, V3

• V1 = _________, V2 = _______, V3 = _________

• Power Calculation

• P1 = _________, P2 = __________, P3 = _________

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R1

100Ω

R2

330Ω R3

470Ω

Et = 100V

Parallel Circuit Calculations

• What is the total resistance Rt?

• Rt = 1/(1/R1 + 1/R2 + 1/R3) Ω = ______________________

• Voltage drops: V1, V2, V3

• Et = V1 = V2 = V3 = _________

• What is I1, I2, I3, and It?

• It = Et/Rt = _______ mA = I1 + I2 + I3 = __________

• I1 = Et/R1 = _______ mA, I2 = Et/R2 = ___________

• I3 = Et/R3 =_____________

• Power Calculation (P = E2/R)

• P1 = _________, P2 = __________, P3 = _________

• Pt = It* Et = P1 + P2 + P3 = ____________

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R1

100Ω

R2

330Ω

R3

470Ω

Et = 100V

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Combinational Circuits

• What is the total resistance Rt?

• Rt = (R2 || R3) + R1 = ______________________

• What is I1, I2, I3, and It?

• It = Et/Rt = _______ mA

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R1

100ΩR2

330Ω

R3

470Ω

Et = 100V

Combinational Circuits

• What is the total resistance Rt?

• Rt = (R2 || R3) + R1 = ______________________

• What is I1, I2, I3, and It?

• It = Et/Rt = _______ mA

• V1 = I1 * R1 = It * R1 = _________

• V2 = V3 = Et – V1 = __________

• I2 = V2/R2 =____________, I3 = V3 /R3 = _____________

• Power Calculation (P = E2/R)

• P1 = _________, P2 = __________, P3 = _________

• Pt = It* Et = P1 + P2 + P3 = ____________

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R1

100ΩR2

330Ω

R3

470Ω

Et = 100V

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Maximum Power Transfer

Maximum Power Transfer. • A voltage source E = 120 v with an

internal resistance of Rs of 50

ohms supplying a load of

resistance RL .

Q1 - Find the value of load resistance RL

that will result in the maximum possible

power being supplied by the source to

the load.

Q2 – How much power be supplied in this

case?

Q3 – Plot the power supply to the load as

a function of the load resistance RL.

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RL = ? ohms

Rs = 50

ohm

E = 120VI

Maximum Power Transfer

Maximum Power Transfer.

Q1 - Find the value of load

resistance RL that will result in

the maximum possible power

being supplied by the source to

the load.

PL = I2 RL,

where I is the current passing

through the circuit.

I = E/Rtotal = E/(Rs + RL)

Array data for MALAB plottingRL – a vector

E and Rs are scalars

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RL = ? ohms

Rs = 50

ohm

E = 120VI

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Maximum Power Transfer

Maximum Power Transfer.

• MATLAB program

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0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80Max Power Transfer

Load resistance RL

Pow

er

- W

att

s

%maxPower.m

Rs = 50;

E = 120;

RL = 1:1:100;

I = E./(Rs + RL);

% NOT I = E/(Rs + RL)

% -- for Scalar calculation

PL = (I.^2) .* RL;

% NOT PL = I^2 * RL

% -- for Scalar calculation

plot(RL, PL), grid on

title('Max Power Transfer');

xlabel('Load resistance RL');

ylabel('Power - Watts');

Maximum Power Transfer

Maximum Power Transfer.

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• Answers

• Q1 – Find the value of RL for Pmax to occur– RL = 50 ohms results a PL

max of 72 watts

• Q2 – How much power be supplied in this case?– PL consume 72 Watt,

– Rs will also receive the same 72 Watts inside the power supply

– Power supplied is 144 watts

• Q3 – Plot the PL(RL)

72 watts

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AC 120 V, 60 Hz Voltage and Current

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035-200

-150

-100

-50

0

50

100

150

200

Time sec

Volt/A

mpere

% MATLAB program

% sinewave2.m

Vm = 170;

Vrms = Vm/sqrt(2);

f = 60;

T = 1/f;

dt = T/100;

t = 0: dt: 2*T;

w = 2*pi*f;

vt = Vm*sin(w*t);

Im = 30;

Irms = Im/sqrt(2);

theta = pi/6;

it = Im * sin(w*t - theta);

plot(t, vt, t, it), grid on

xlabel('Time sec'), ylabel('Volt/Ampere');15

𝑣 𝑡 = 170 sin 𝜔𝑡 = 120 2 sin(𝜔𝑡)

𝑖 𝑡 = 30 sin 𝜔𝑡 −𝜋

6= 21.21 2 sin(𝜔𝑡 −

𝜋

6)

AC 120 V, 60 Hz Voltage and Current

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035-200

-150

-100

-50

0

50

100

150

200

Time sec

Volt/A

mpere

% MATLAB program

% sinewave2.m

Vm = 170;

Vrms = Vm/sqrt(2);

f = 60;

T = 1/f;

dt = T/100;

t = 0: dt: 2*T;

w = 2*pi*f;

vt = Vm*sin(w*t);

Im = 30;

Irms = Im/sqrt(2);

theta = pi/6;

it = Im * sin(w*t - theta);

plot(t, vt, t, it), grid on

xlabel('Time sec'), ylabel('Volt/Ampere');16

𝑣 𝑡 = 170 sin 𝜔𝑡 = 120 2 sin(𝜔𝑡)

𝑖 𝑡 = 30 sin 𝜔𝑡 −𝜋

6= 21.21 2 sin(𝜔𝑡 −

𝜋

6)