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.

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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

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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:

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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)

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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)]

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Discharging a capacitor

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House Wiring