Download 19-3 Kirchhoff`s Rules

Chapter 19
DC Circuits
Objective of the Lecture
• Explain Kirchhoff’s Current and Voltage
Laws.
• Demonstrate how these laws can be used to
find currents and voltages in a circuit.
• Explain how these laws can be used in
conjunction with Ohm’s Law.
19.3 Kirchhoff’s Rules
Some circuits cannot be broken down into
series and parallel connections.
Kirchhoff’s Rules
• Many practical resistor networks cannot be reduced to simple series-parallel
combinations (see an example below).
• Terminology:
-A junction in a circuit is a point where three or more conductors meet.
-A loop is any closed conducting path.
junction
Loop 2
i
i
i2
i1
i
Loop 1
i
i2
junction
Basic Laws of Electric Circuits
Nodes and Branches:
A branch: A branch is a single electrical element or device.





A circuit with 5 branches.
A node: A node can be defined as a connection point between
two or more branches.




2
A circuit with 3 nodes.
Kirchhoff's Rules
Junction rule. The sum of the magnitudes of
the currents directed into a junction equals
the sum of the magnitudes of the currents
directed out of the junction.
Loop rule. Around any closed circuit loop, the
sum of the changes in potential around any
closed path of a circuit must be zero.
Kirchhoff’s Current Law
• Or KCL for short (Junction Rule)
– Based upon conservation of charge – the
algebraic sum of the charge within a system
can not change.
N
 in  0
Where N is the total
number of branches
connected to a node.
n 1
i
enter
node

i
leave
node
Kirchhoff’s Voltage Law
• Or KVL for short (Loop Rule)
– Based upon conservation of energy – the
algebraic sum of voltages dropped across
components around a loop is zero.
M

v0
m 1
v
drops
Where M is the total
number of branches in
the loop.
  v rises
Junction Rule
Junction rule. The sum
of the magnitudes of the
currents directed into a
junction equals the sum
of the magnitudes of the
currents directed out of
the junction.
Application of Junction Rule
A galvanometer is a type of sensitive ammeter: an
instrument for detecting electric current.
Q: A galvanometer
with a full-scale limit of
0.100 mA is to be used
to measure a current
of 60.0 mA. How much
current will pass
through the shunt
resistance R?
A: 60.0 – 0.1 = 59.9 mA
Current Measurement
Multi-Loop Circuits
 Assume we have a junction point a
 We define a current i1 entering junction a and two
currents i2 and i3 leaving junction a
 Kirchhoff’s Junction Rule tells us that
i1 = i2 + i3
2/13/07
184 Lecture 20
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19.3 Kirchhoff’s Rules
For these circuits we use Kirchhoff’s rules.
Junction rule: The sum of currents entering a
junction equals the sum of the currents
leaving it.
19.3 Kirchhoff’s Rules
Loop rule: The sum of
the changes in
potential around a
closed loop is zero.
Loop Rule
Loop rule. Around any closed circuit loop,
the sum of the potential drops equals the
sum of the potential rises.
Voltage Measurement
Putting it all together
Kirchhoff’s Rules
 Kirchhoff’s
junction rule
• The algebraic sum of the currents into any junction is zero:
 I  0 at any junction
Kirchhoff’s Rules
 Kirchhoff’s
loop rule
• The algebraic sum of the potential differences in any loop, including
those associated with emfs and those of resistive elements, must equal
zero.
V  0 for any loop
Kirchhoff’s Rules

Rules for Kirchhoff’s loop rule
 I  0 at any junction
V  0 for any loop
Kirchhoff’s Rules

Rules for Kirchhoff’s loop rule (cont’d)
Kirchhoff’s Rules

Solving problems using Kirchhoff’s rules
Kirchhoff’s Rules

Example 1
Kirchhoff’s Rules

Example 1 (cont’d)
Kirchhoff’s Rules

Example 1 (cont’d)
Kirchhoff’s Rules
Find
all the currents
 Example
2 including directions.
Loop 2
i
i
i2
i1
i
Loop 1
i
Loop 1
0 = +8V + 4V - 4V - 3i - 2i1
0 = 8 - 3i1 - 3i 2 - 2i1
0 = 8 - 5i1 - 3i 2
multiply by 2
i = i1+ i2
i2
Loop 2
- 6i 2 + 4 + 2i1 = 0
 6i2  4  2(1A)  0
- 6i 2 + 16 - 10i1 = 0
0 - 12 + 12i1 = 0
i 2 = 1A
i1 = 1A
i = 2A
Ammeter and Voltmeters
 A device used to measure current is called an ammeter
 A device used to measure voltage is called a voltmeter
 To measure the current, the ammeter must be placed in the
circuit in series
 To measure the voltage, the voltmeter must be wired in
parallel with the component across which the voltage is to
be measured
Voltmeter in parallel
High resistance
since you do not
want current going
through it
Ammeter in series
Low resistance
since current
goes through it
27
Practice Problem p.548 #23
 Calculate the current in the circuit of Fig. 19–43
and show that the sum of all the voltage changes
around the circuit is zero.
Practice Problem p.548 #24
19.3 Kirchhoff’s Rules
Problem Solving: Kirchhoff’s Rules
1. Label each current.
2. Identify unknowns.
3. Apply junction and loop rules; you will
need as many independent equations as
there are unknowns.
4. Solve the equations, being careful with
signs.
Homework:
Problems 25 and 32
Closure:
Kahoot:
19-3