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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
George Washington University
Direct Current (DC) & Alternating Current (AC)
DC: uni-directional movement of electric charges
AC: the direction of the movement of electric charges reverses periodically
George Washington University
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
George Washington University
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
George Washington University
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
George Washington University
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
George Washington University
Examples
Online examples for resistances
George Washington University
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
)
George Washington University
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
George Washington University
Examples
Online examples for resistances
George Washington University
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 )
George Washington University
Examples
Online examples for resistances
George Washington University
Exercises
George Washington University
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 = ?
George Washington University
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
George Washington University
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 = ?
George Washington University
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 = ?
George Washington University
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 = ?
George Washington University
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
George Washington University
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