george washington university dc circuits lab professor ahmadi ， xin xu ece 1020

George Washington University

DC Circuits LabProfessor Ahmadi ， Xin Xu

ECE 1020

George Washington University

Outline

DC and AC circuit

Omh’s Law

Equivalent resistance in series and parallel cuicuits

Exercises & Homework

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Direct Current (DC) & Alternating Current (AC)

DC: uni-directional movement of electric charges

AC: the direction of the movement of electric charges reverses periodically

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Ohm’s Law

€

V = I × RQuantifying the relationship between voltage and

current

V voltage, volt (V)

I current, amp (A)

R resistance ohm (Ω)V R

I

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An Example

3V = I x 1000 Ω

Solve for I:

I=3V / 1000 Ω = 3milliAmps

3V R = 1K Ω

I = ? Amps

Determine the current using Ohm’s Law

€

V = I × R

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Resisters in Series

V

R1 I

R2

R3

€

V1 = I1 × R1

V2 = I2 × R2

V3 = I3 × R3

€

I1 = I2 = I3 = I

Apply Ohm’s Law on each resister

Just one path, currents are equal

Voltage drops can be added up

€

Req = R1 + R2 + R3

€

V = I1R1 + I2R2 + I3R3 = I(R1 + R2 + R3)

Equivalent resistance

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Principles for Resisters in Series

V

R1 I

R2

R3

€

Req = R1 + R2 + R3

Current remains same in one circle

Voltage can be added up

Equivalent Resistance equal to sum of all resisters in series

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Examples

Online examples for resistances

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Resisters in Parallel

V R1

I

R2 R3

€

V1 = I1 × R1

V2 = I2 × R2

V3 = I3 × R3

€

V1 =V2 =V3 =V

Apply Ohm’s Law on each resister

Current is divided to 3 paths

Voltages are same on each path

€

Req =1

1

R1

+1

R2

+1

R3

Equivalent resistance

€

I = I1 + I2 + I3 =V1

R1

+V2

R2

+V3

R3

=V × (1

R1

+1

R2

+1

R3

) =V /(1

1

R1

+1

R2

+1

R3

)

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Principles for Resisters in Parallel

Voltages remain same in parallel paths

Current can be added up

V R1

I

R2 R3

€

Req =1

1

R1

+1

R2

+1

R3

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Examples

Online examples for resistances

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Combined

€

Req =1/(1

R2

+1

R3

)

Find equivalent resistance for parallel resistances

V

R1

I

R2 R3

V

R1

I

Req

Solve the serial circuit

€

V = I × (R + Req )

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Examples

Online examples for resistances

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Exercises

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Exercises – Ohm’s Law

Given a circuit with a power source V = 9V,find the loop current if the resistance is 100 Ohm

Find the loop current by hand, and then build the circuit using the online interactive simulator

What is the current if the resistance is doubled

What is the current if the resistances is reduced by 50%

What is the current if the voltage is doubled?

What is the current if the voltage is reduced by 50%

€

V = 9V ,R1 =100Ω,I = ?

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Exercises - series

Given a circuit with a power source V = 12V,find the loop current if resistances are in series

Find the loop current by hand, and then build the circuit using the online interactive simulator

What is the loop current if all resistances are doubled

What is the loop current if all resistances are reduced by 50%

€

R1 = 300Ω,R2 =150Ω,R3 = 600Ω

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Exercises - parallel

Given a circuit with a power source V = 12V,find the loop current I if 2 resistances are connected in parallel

€

R1 =100Ω,R2 =100Ω

V=12V R1 R2

Find the current I by hand, and then build the circuit using the online interactive simulator

What is the current I if all resistances are doubled?

What is the current I if all resistances are reduced by 50%

I = ?

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Exercises - parallel

Given a circuit with a power source V = 12V,find the loop current if 3 resistances are connected in parallel

€

R1 =100Ω,R2 =100Ω,R3 =100Ω

V R1 R2 R3

Find the current I by hand, and then build the circuit using the online interactive simulator

What is the current I if all resistances are doubled

What is the current I if all resistances are reduced by 50%

I = ?

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Exercises – series/parallel

Given a circuit with a power source V = 5V,find the loop current I if R1, R2 are connected in parallel, and then connected to R3 in series

€

R1 =100Ω,R2 =100Ω,R3 = 50Ω

V

R3

R1 R2

Find the current I by hand

Build the circuit using the online interactive simulator to verify your results

I = ?

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Exercises – series/parallel

Given a circuit with a power source V = 5V,find the loop current if R1, R2, R3 are connected in parallel, and then connected to R4 in series

€

R1 = 300Ω,R2 = 300Ω,R3 = 300Ω,R4 =100Ω

V R1 R2 R3

R4

Find the loop current I by hand

Build the circuit using the online interactive simulator to verify your results

I = ?

George Washington University

Exercises – series/parallel

Find the loop current I by hand, and then build the circuit using the online interactive simulator

V

R1

I = ?

R2

R3 R4

€

V = 9V

R1 = 200Ω,R2 = 50Ω

R3 = 600Ω,R4 = 300Ω

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Homework

Find the loop current I, and voltage and current for each resistor

Build the circuit using the online interactive simulator to verify your results

V

R1

R2

R3 R4

€

V = 9V

R1 =100Ω,R2 =100Ω

R3 = 200Ω,R4 = 400Ω

I = ? €

V1,I1;V2,I2;V3,I3;V4,I4