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

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.

Current Measurement

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.

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:

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

Kirchhoff’s Rules Rules for Kirchhoff’s loop rule

junction any at 0I

loopany for 0V

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)

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.

Homework:

Problems 25 and 32

Closure:

Kahoot:

19-3