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.
Kirchhoff’s Rules
Loop 1
Loop 2
i i
i
i
i1
i2
i2
• 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
junction
Basic Laws of Electric CircuitsNodes and Branches:
A node: A node can be defined as a connection point betweentwo or more branches.
A branch: A branch is a single electrical element or device.
A circuit with 5 branches.
A circuit with 3 nodes.
2
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.
nodenode
1
0
leaveenter
N
nn
ii
i Where N is the total number of branches connected to a 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.
rises drops
M
1m
v v
0 v Where M is the total number of branches in the loop.
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
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
A galvanometer is a type of sensitive ammeter: an instrument for detecting electric current.
2/13/07 184 Lecture 20 12
Multi-Loop Circuits Multi-Loop Circuits Multi-Loop Circuits 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
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.
Loop Rule
Loop rule. Around any closed circuit loop, the sum of the potential drops equals the sum of the potential rises.
Kirchhoff’s Rules Kirchhoff’s junction rule
• The algebraic sum of the currents into any junction is zero:
junction any at 0I
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. loopany for 0V
Find all the currents including directions.
Loop 1
Loop 2
i i
i
i
i1
i2
i2
Kirchhoff’s Rules Example 2
0)1(246 2 AiLoop 1 Loop 2
multiply by 2
i = i1+ i2
27
Ammeter and VoltmetersAmmeter and VoltmetersAmmeter and VoltmetersAmmeter 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 parallelHigh resistancesince you do not
want current goingthrough it
Ammeter in seriesLow resistancesince current
goes through it
Practice Problem p.548 #23Practice Problem p.548 #23Practice Problem p.548 #23Practice 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 #24Practice Problem p.548 #24Practice Problem p.548 #24Practice 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.
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