Section 04
Ohm’s Law
A current through a resistor is proportional to the voltage across its terminals
R I V or
R I
V = ⋅ =
OC circuit
open I
R
SC circuit short
I R
∞
=
→
=
∞
→ 0
0
Short a 1.5 battery, what will happen?
Internal Resistance
If you short a 1.5V battery, how much current will pass?
Electrical & Computer Engineering King Abdulaziz University Slide 97
Overloading
Question
What is the total current drawn from the source?
Electrical & Computer Engineering King Abdulaziz University Slide 99
R A I V R L
5 2 10
5 3 2 3 4 //
4
=
=
=
Ω
= +
= +
=
Voltage Divider
2 1
1
1 R R
v R v s
= +
2 1
2
2 R R
v R v s
= +
Current Divider
Electrical & Computer Engineering King Abdulaziz University Slide 101
2 1
2
1 R R
I R I T
= +
2 1
1
2 R R
I R I T
= +
Multiple Loads
Combine Parallel Loads
Multiple Loads
Electrical & Computer Engineering King Abdulaziz University Slide 103
23 1
23
1 R R
I R I T
= +
23 1
1
4 R R
I R I T
= +
3 2
23
R // R
R =
Multiple Loads
3 2
3 4
2 R R
I R
I = +
3 2
2 4
3 R R
I R
I = +
Current Divider
Electrical & Computer Engineering King Abdulaziz University Slide 105
k p T k
n p
R I R I
R R
R R
=
= 1 // 2 // L //
Process Check
Calculate all currents in the circuit..
What is your plan?!
Multiple Sources
What if more than one source in the circuit?
How to solve for all currents?
Electrical & Computer Engineering King Abdulaziz University Slide 107
Nodes and Loops
A Node
a point in a circuit where 3 or more elements meet
Nodes and Loops
How many nodes in the circuits?
Electrical & Computer Engineering King Abdulaziz University Slide 109
Nodes and Loops
A Loop:
a closed ring in a planer circuit
Planer Circuit
Electrical & Computer Engineering King Abdulaziz University Slide 111
Voltage Drop
A current passing through a load generates a voltage drop
R i v = ⋅
Z
i
v = ⋅
KVL and KCL
(nodes, loops, planner circuit, voltage drop) then what?
To solve for all currents and volts in a circuit:
KVL: Kirchhoff’s Voltage Law
the algebraic sum of voltages in a loop is zero
KCL: Kirchhoff’s Current Law
the algebraic sum of currents into a node is zero
Electrical & Computer Engineering King Abdulaziz University Slide 113
Circuit Analysis
1. count nodes minus one (possible ground) 2. mark a current for each branch
name and direction
3. write KCL equations for each node 4. count the loops
5. write the KVL equations for each loop
6. solve for all unknowns
Example
Electrical & Computer Engineering King Abdulaziz University Slide 115
1
0
++++ −−−−
++++ ++++ ++++
−−−−
−−−−
−−−−
1 2
Example
1
0
++++ −−−−
++++ ++++ ++++
−−−−
−−−−
−−−−
3 2
: I 1 I I
KCL = +
0 12
4 5
0 5
6 5 .
: 1 1 3
= +
+
−
= +
+
−
I I
I
I
KVL I I mA
mA I
mA I
5 . 116
4 . 36
9 . 152
3 2 1
=
=
=
⇒
Example
Electrical & Computer Engineering King Abdulaziz University Slide 117
8 branches 8 currents I 1 ..I 8 8 equations 4 nodes 4 eqs
4 loops 4 eqs
