Download Kirchhoff`s Laws Review A more complex circuit …

Kirchhoff’s Laws
Reminder: there will be a Quiz on
Chapter 1 next Monday (Jan.23)
Review
Electric Circuit
Voltage
Current
Ohm’s Law
>
i
+
_
Vs +
R
v
_
A more complex circuit …
R1
a
R2
b
R3
v1
c
v2
d
Objective:
determine voltage and current in a circuit
Kirchhoff’s Voltage Law
Kirchhoff’s Current Law
1
Preliminaries
Branch
Node
Loop
Voltage drop / rise
Voltage Drops & Rises Defined
+
5V
a
b
The following statements are true and equivalent
ØThere
is a 5 V voltage drop from a to b
is a 5 V voltage rise from b to a
is a -5 V voltage rise from a to b
ØThere is a -5 V voltage drop from b to a
ØThere
ØThere
• The first expression is the most common
• In most cases, we will be concerned with voltage drops
Kirchhoof’s Voltage Law
(KVL)
“The algebraic sum of all voltage drops
around any closed loop is zero”
M
∑v
m
=0
m=1
M : numberof voltages in theloop
vm : mth voltage
– Satisfied around all loops of a circuit
–
A statement about energy conservation
2
Kirchhoof’s Current Law
(KCL)
“The algebraic sum of currents entering a node is
zero”
N
∑i
n
=0
n =1
N : number of branches connected to the node
i n : n th current enteringthe node
–
Satisfied at all nodes of a circuit
– A statement about charge conservation
– Applies to larger, closed region of a circuit
(“supernodes ”)
Kirchhoff’s Current Law
a. i 2
b.
i1
h.
i12
i3
i10
.i
i8
.i
i5
Supernode
c.
i4
.d
i11
.
g
i7 . i6
9
e
f
Application of Kirchhoff’s
Laws
.
a
5V
2Ω
4Ω
.b
8Ω
_+
.c
- 3V
+
.d
3