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Lecture PowerPoints
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 27
Direct-Current Circuits
Main Points of Chapter 27
• emf and its meaning
• Internal resistance
• Kirchhoff’s loop and junction rules
• Multi-loop circuits
• Measuring instruments
• RC circuits
27-1 EMF
• An emf is a source of energy in a circuit that
causes charges to move
• Circuit with battery and resistor: potential
difference between battery terminals causes
current to flow through resistor
• Chemical reactions inside battery send
charge back to terminal
• Definition of emf:
(27-1)
27-1 EMF
Internal resistance
• Battery with emf of 9 V will not
necessarily have 9 V potential
difference between its terminals, due
to internal resistance:
(27-5)
where r is the internal resistance.
27-2 Kirchhoff’s Loop Rule
• Single-loop circuit has just one path for current
• Beginning at any point in circuit and going all the
way around must involve a total potential change
of zero (you come back to where you started)
• When moving in the direction of the current,
potentials decrease across resistors and increase
across batteries
• Sum of potential changes around a closed path is
zero:
(27-9)
27-2 Kirchhoff’s Loop Rule
Basic single-loop circuit:
27-2 Kirchhoff’s Loop Rule
• When moving around the loop
opposite to the direction of the current,
potential difference increases across
resistors and decreases across
batteries
• Across a capacitor from – side to +
side, potential increases; in other
direction it decreases
27-3 Kirchhoff’s Junction Rule
• All the current that comes into a junction
must go out again
• The algebraic sum of the currents
entering a junction equals zero
(27-11)
27-3 Kirchhoff’s Junction Rule
• Solving multi-loop circuits:
• Use both junction and loop equations
• Some will be redundant
• Need as many independent equations as
there are unknown currents
• A circuit with n junctions will have n – 1
independent junction equations
27-3 Kirchhoff’s Junction Rule
Example:
• This circuit requires three independent equations
• This circuit has two junctions; two of the
equations will have to be loop equations
27-4 Measuring Instruments
• Ammeter measures current
• Voltmeter measures
potential difference
• Ohmmeter measures
resistance
• Multimeter does all three
27-4 Measuring Instruments
• Ammeter: connect in series; very small
resistance compared to other circuit
elements, so current is not affected
• Voltmeter: connect in parallel; large
resistance, so voltage is not affected
• Internal resistance of voltmeter can be
varied to allow different voltage scales
27-5 RC Circuits
RC circuit with battery and switch
• Switch at position A: battery charges capacitor
• Switch at position B: capacitor discharges
through resistor
27-5 RC Circuits
Current stops flowing when capacitor is fully
charged:
Charge as a function of time:
(27-22)
Current as a function of time:
Time constant:
(27-23)
27-5 RC Circuits
Current and charge as functions of time
27-5 RC Circuits
Discharging: charge
decreases with same
time constant
Summary of Chapter 27
• Sources of emf are sources of electric
energy
• emf is defined by work it can do:
(27-1)
• Kirchhoff’s loop rule:
(27-9)
• Kirchhoff’s junction rule:
(27-11)
Summary of Chapter 27, cont.
• Capacitor being charged by battery has
charge and current:
(27-22)
(27-23)
• When discharging,
(27-26)