Electric Circuits I “Dr. Ahmed El-Shenawy”
Electrical Circuits I
Lecture 2
<Dr Ahmed El-Shenawy>
Electric Circuits I “Dr. Ahmed El-Shenawy”
KCL and KVL
Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) are the
fundamental laws of circuit analysis.
Gustav Kirchoff
was an 18th century
German
mathematician
Electric Circuits I “Dr. Ahmed El-Shenawy”
KCL
The sum of all currents entering a
node is zero,
or
The sum of currents entering a
node is equal to sum of currents
leaving a node.
i1  i2  i3  i4  i5  0
or
n
i
j
0
j 1
i1  i 2  i 4  i3  i5
A node is a point where two or more circuit elements are connected
together.
Electric Circuits I “Dr. Ahmed El-Shenawy”
i1
node
i2
i1 flows into the node
i2 flows out of the node
i3 flows out of the node
i1 = i2 + i3
 This equation can also be written in the following form:
i1 - i2 - i3 =0
i3
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example
How much are the currents i1 and i2 ?
10 mA
node
i1
4 mA
3 mA
+
_
4 mA + 3 mA + 7 mA = 14 mA
i2 = 10 mA – 3 mA = 7 mA
i1 = 10 mA + 4 mA = 14 mA
i2
Electric Circuits I “Dr. Ahmed El-Shenawy”
KVL
 Kirchhoff’s voltage law tells us how to handle voltages in an electric
circuit.
Kirchhoff’s voltage law basically states that the algebraic sum of the
voltages around any closed path (electric circuit) equal zero.
n
v
j
0
j 1
Arrows are sometimes used to represent voltage differences; they point
from low to high voltage.
i
i
+
v
-
≡
v
Electric Circuits I “Dr. Ahmed El-Shenawy”
i
+
v1
–
+
_
– v1 + v2 + v3 = 0
or
v1= v2 + v3
+
v2 –
+
v3
–
+
v4
–
– v1 + v2 + v4 = 0
or
v1= v2 + v4
v3= v4
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example
If v1 = 10 V and v5 = 2 V, what are v2, v3, and v4?
+ v3 –
+
v1 = 10 V
–
+
_
+
v2
+
v4
+
v5= 2 V
–
–
–
v2 = 10 V
v3 = 10 V – 2 V = 8 V
v4 = 2 V
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example:
The voltage v1 and v2 in the circuit shown are 512.41V and 330.05V
respectively.
 Find the power supplied by each voltage source.
Show that the total power supplied equals the total power dissipated in the
resistors
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example:
Find v0 in the circuit shown.
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example:
The current in the 12Ω resistor in the circuit shown is 1 A, find vg.