Download Chapter - 2nd Semester Notes

Basic Electrical Circuits &
Machines (EE-107)
Course Teacher
Shaheena Noor
Assistant Professor
Computer Engineering Department
Sir Syed University of Engineering & Technology.
VOLTAGE AND CURRENT LAWS
In this chapter, we discuss the behavior of
electric circuits. Two simple laws, Kirchhoff’s
Current law and Kirchhoff’s voltage law form
the foundation for circuit analysis
procedure.
Voltage and Current Laws
• Circuits
– Series Circuit
– Parallel Circuit
Series Circuits
“Two components are connected in series if
they have exactly one common terminal and if
no other component has a terminal that
shares that common connection.”
Figure (a)
Figure (b)
Common terminal
R1
R2
R
Common
terminal
V
Series Circuits
• A series path is one in which every component in the path
is in series with another component.
Analysis of Series Circuit:
• Important property is that the current is the same in every
series-connected component.
• Another fact is its total resistance.
• Total resistance is the sum of all the series-connected
resistances.
RT or Req = R1 + R2 + R3 + . . .
• When a voltage source is connected in series circuit, the
total current produced by that source is from Ohm’s Law.
Series Circuits
• Example # 01:
Let R1 = 2Ω; R2 = 1 Ω; V = 5Volts; I = ?
R1
V
R2
• Example # 02:
Find I and voltage across each resistor.
I
R1 = 12 Ohm
R2 = 6 Ohm
24V
R3 = 10 Ohm
Kirchhoff’s Voltage Law (KVL):
It states that “ The algebraic sum of the voltages
around any closed path is zero.”
V1 + V2 + V3 + . . . . . . . + VN = 0
OR
• “ The sum of the voltage drops around any
closed loop equals the sum of the voltage
rises around the loop.”
Kirchhoff’s Voltage Law (KVL):
• Example 3.2
Find vx and i .
7V
+
5V
i
Vx
-
100 Ohm
Drill Problem 3.2 ( page 34)
Determine i and vx for the figure given below.
1V
+
3V
i
Vx
-
10 Ohm
Kirchhoff’s Voltage Law (KVL):
• Other Examples:
Drill Problem 3.4 (page 37)
• In the circuit, vs1 = 120V, vs2 = 30V, R1 = 30Ω and R2 =
15Ω. Compute the power absorbed by each
element.
R1
Vs1
Vs2
R2
For Dependent Sources:
Drill Problem 3.5 (page 38)
• In the Circuit , find the Power absorbed by each of
the five elements in the circuit.
12 V
+
30 Ohm Vx
-
8 Ohm
7 Ohm
+
-
4Vx
Drill Problem 3.9 ( page 45)
• Determine i in the given circuit.
5V
15 Ohm
5V
25 Ohm
i
5V
5 Ohm
Open Circuit
• Break in a circuit path.
• No current can flow through an open.
• Since no current can flow through it, an open circuit
has an infinite resistance (R = ∞)
I = V/R = ?
• Important: It is a common error that since the
current in an open circuit is zero, the voltage across
the open must also be zero.
For Example:
What is the voltage ‘V’ across the switch
terminal when the switch is open.
20 Ohm
+
V
-
60 V
40 Ohm
Voltage Divider Rule (VDR)
R1
+
V1
-
R2
+
V2
-
E
I=?
V1 = ?
V2 = ?
For Example:
• Use VDR to find V200Ω and V150 Ω.
• Verify this using KVL
100 Ohm
200 Ohm
36V
150 Ohm
50 Ohm
Parallel Circuits:
• Two components are connected in parallel
when they have 2 common terminal.
R2
• For Example:
R1
R1
R2
R3
R3
V
R1
R2
V
R2
R1
R4
R3
Parallel Circuits:
Analysis of Parallel Circuits:
• Important property of parallel circuit is that
every parallel-connected component has the
same voltage across it.
V
R1
R2
For Example:
• Find the current in each resistor.
I1
48V
I2
R1
2 Ohm
I3
R2
4 Ohm
R3
6 Ohm
Parallel Circuits:
• Resistance in Parallel:
• For 2 resistors (only)
V
R1
R2
Kirchhoff’s Current Law (KCL):
It states that:
• “ The algebraic sum of the current entering
any node is zero”
OR
• “The sum of all currents entering a junction or
any portion of a circuit equals the sum of all
currents leaving the same.”
iA
iD
iB
ic
Example
• Find the current in the 150Ω resistor
I1 = 0.8A
270 Ohm
I2 = 0.2A
100 Ohm
I4 = ?
I3 = 0.1A
330 Ohm
150 Ohm
Q-5 (a) (page 55)
• Find ix in each of the circuits.
4A
V
ix
1A
Q6 (page 55)
• Find ix; if iY = 2A and iZ = 0A
• Find iY; if iX = 2A and iZ = 2iYA
5A
iX
iY
3A
iZ
Current Division Rule (CDR):
• Consider 2 parallel resistor
I
I1
I2
R1
R2
• Note: Parallel resistors must be branches
between the same pairs of nodes.
Example:
• Find I1 and I2 using the current divider rule.
• Verify the result using KCL
R1 = 470 Ohm
160mA
I1
I2
R2 = 330 Ohm
Example 3.13 (Page 52)
• Find current across 3Ω resistor using CDR.
4 Ohm
12V
6 Ohm
3 Ohm
Short Circuit
• A short circuit is a path of zero resistance.
• A component is said to be short-circuited
when there is a short circuit connected in
parallel with it.
Iss = ?
R
IR = ?
I