chapter 25 – dc circuits · circuits and symbols • electric circuits are portrayed with...
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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.
Slide 25-3 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
CT 29.9 Two identical resistors are wired in series (one behind the other). They are attached to a battery a current is flowing through the circuit.
The current in the second resistor is _____ the current in the first resistor
A: Equal to B: Half C: Smaller than, but not necessarily half
Slide 25-4 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Kirchoff’s Loop Rule
• The sum of all voltage drops and gains along any circuit loop is 0.
Vemf − IR1 − IR2 = 0
Voltage between resistors? V = Vemf − IR1 = 12 V − (2 A)(2 Ω) = 8 V
I =Vemf
R1 + R2=
12 V6 Ω
= 2 A
Vemf +
i
∆Vi = 0
E · dl = 0
Resistors in series • When circuit components are connected in series, current
from one component all flows into the next component.
• With two resistors in series, the current I results in voltage drops IR1 and IR2:
• These sum to the battery emf:
• Therefore the two resistors behave as a single resistor of resistance R1 + R2.
• In general, resistors in series add:
Rseries = R1 + R2 + R3 + …
Vemf = IR1 + IR2 = I(R1 + 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)
Resistors in Parallel • Kirchoff’s Junction Rule: The sum of the currents into
any junction is zero (conservation of charge)
• The voltage across each resistor is the batter emf. Thus
• Therefore the two resistors behave as a single resistor whose resistance is R = 1/(1/R1+1/R2).
1Rparallel
=1R1
+1R2
+1R3
+…
I = I1 + I2
I1 =Vemf
R1I2 =
Vemf
R2
I = Vemf
1
R1+
1R2
In General:
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
Question 32.12 Circuits I
1) circuit I
2) circuit II
3) both the same
4) it depends on R
The lightbulbs in the circuits below are identical with the same resistance R. Which circuit produces more light? (brightness ⇐⇒ power)
Slide 25-10 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
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.
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.
E
3E2E
2 3E
Capacitors in circuits
• Capacitors introduce time-dependent behavior to circuits. • The voltage across a capacitor is proportional to the
charge on the capacitor.
∆VC = q/C
The RC circuit • When switched is closed, what is current
as a function of time? • As the capacitor charges,
VC increases and the voltage across the resistor (Vab) decreases, and current decreases.
I(t) =Vemf
Rexp(−t/RC)
I =dq
dt=
Vemf − Vc
R=
Vemf − q/C
R
dq
VemfC − q=
dt
RC
q(t) = VemfC [1− exp(−t/RC)]
Slide 25-15 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Discharging a capacitor
Slide 25-16 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
House Wiring