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Chapter 25 – DC Circuits
Circuits and symbols
•  Electric circuits are portrayed with diagrams using
standard symbols, showing interconnections among their
components:
•  Most circuits contain a
source of “electromotive
force,” or emf, a device
like a battery that supplies
a voltage.
Kirchoff’s Loop Rule
Vemf +
�
∆Vi = 0
i
•  the sum of the EMFs in any closed loop is equal to the sum of the
potential drops in that loop.
Vemf − IR1 − IR2 = 0
Vemf
12 V
I=
=
=2A
R 1 + R2
6Ω
Voltage between resistors?
V = Vemf − IR1 = 12 V − (2 A)(2 Ω) = 8 V
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Slide 25-3
Resistors in series
•  When circuit components are connected in series, current
from one component all flows into the next component.
•  Therefore the current through series components is the same.
•  With two resistors in series, the
current I results in voltage drops
IR1 and IR2:
•  These sum to the battery emf:
Vemf = IR1 + IR2 = I(R1 + R2 )
•  Therefore the two resistors behave
as a single resistor of resistance
R1 + R2.
•  In general, resistors in series add:
Rseries = R1 + R2 + R3 + …
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-5
•  Kirchoff’s Junction Rule: The sum of the currents into
any junction is zero (conservation of charge)
I = I1 + I2
•  Resistors in Parallel:
•  With two resistors in parallel,
the battery emf drives currents
Vemf
Vemf
I2 =
I1 =
R2 �
R1 �
I = Vemf
1
1
+
R1
R2
•  Therefore the two resistors behave
as a single resistor whose
resistance is R = 1/(1/R1+1/R2).
Clicker question
• 
Rank order the voltages across the identical resistors R
at the top of each circuit shown. In (a) the second
resistor has the same resistance R, and in (b) the gap is
an open circuit (infinite resistance).
A.  (c) > (b) > (a)
B.  (c) > (a) > (b)
C.  (b) > (c) > (a)
D.  (a) > (b) > (c)
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-8
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-9
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-10
Clicker question
• 
The figure shows a circuit with three identical light
bulbs and a battery. What happens to each of the other
two bulbs if bulb C goes out?
A.  Bulb A brightens; bulb B dims.
B.  Bulb B brightens; bulb A dims.
C.  Bulbs A and B both dim.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-12
Clicker question
• 
An ideal voltmeter is connected between points A and B
in the figure. What value does the voltmeter read?
A. 
B. 
C. 
D. 
House Wiring
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-14
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-15
Capacitors in circuits
•  Capacitors introduce time-dependent behavior to circuits.
•  The voltage across a capacitor is proportional to the
charge on the capacitor.
The RC circuit
•  The capacitor voltage VC is initially
zero.
•  As the capacitor charges,
VC increases and the
voltage across the
resistor (Vab) decreases, and current
decreases.
dq
Vemf − Vc
Vemf − q/C
I=
=
=
dt
R
R
Vemf
I(t) =
exp(−t/RC)
R
•  Eventually a steady state is
reached, with zero current
and capacitor voltage equal to the
battery emf.
Discharging a capacitor
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 25-18