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Physics 123
19. DC Circuits
19.1 Resistors in Series and Parallel
19.6 Capacitors in Series and Parallel
19.7 RC Circuit
19.10 Ammeters and Voltmeters
Bulbs in Series and Parallel
L3
L1
L2
L4
A.
B.
C.
D.
L1 and L2 are in series
L1 and L2 are in parallel
L3 and L4 are in series
None of the above
Bulbs in Series and Parallel
L3
L1
L2
L4
L1 and L2 are in series and L3 and L4 are in
parallel
Bulbs in Series and Parallel
L3
L1
L2
L4
A.
B.
C.
D.
I1 = I 2
V1 = V2
I3 = I 4
None of the above
Bulbs in Series and Parallel
L3
L1
L2
L4
Series
I1 = I 2
Parallel
V3 = V 4
Which bulb is brighter?
L1
A.
B.
C.
D.
L2
L1 and L2 are equally bright
L1 is brighter than L2
L2 is brighter than L1
None of the above
Which bulb is brighter?
L1
L2
None of the above. Brightness depends on power
(watts) which is P = VI or P = I2R. In general, L1
and L2 will shine differently unless they are the
same type of bulb. Different bulbs have different
values of filament resistance.
Brightness of Bulbs in Parallel
L3
L4
A.
B.
C.
D.
L3 and L4 are equally bright
L3 is brighter than L4
L4 is brighter than L3
None of the above
Brightness of Bulbs in Parallel
L3
L4
None of the above. Brightness depends on power
(watts) which is P = VI or P = V2 / R. In general,
L1 and L2 will shine differently unless they are the
same type of bulb. Different bulbs have different
values of filament resistance. The bulb with the
smaller resistance will be brighter in this case!
What’s wrong with this picture?
L1
L2
L1
L2
In which circuit is L2 brighter?
In which circuit is L1 brighter?
What’s wrong with this picture?
L1
L2
L1
L2
In which circuit is L2 brighter? … Just kidding!
In which circuit is L1 brighter? … Well, L1 will
not light up without L2 in a series circuit.
Bulbs in Series and Parallel
L3
L3
L4
In which circuit is L4 brighter?
In which circuit is L3 brighter?
Bulbs in Series and Parallel
L3
L3
L4
In which circuit is L4 brighter? … Just kidding!
In which circuit is L3 brighter? L3 will be equally
bright in both circuits … And I am DEAD
SERIOUS. The voltage is the same, the current is
the same , the power is the same, the brightness is
Comparative Brightness
L3
L1
L2
L4
A.
B.
C.
D.
L1 and L3 are equally bright
L3 is brighter than L1
L1 is brighter than L3
None of the above
Bulbs in Series and Parallel
L3
L1
L2
L4
B.
L3 is brighter than L1
The voltage across L3 is greater than the voltage
across L1. Also, the current through L3 is greater
than the current through L1
Example 19.1 . . . Series Circuit
R1 = 3Ω
R2 = 6Ω
V = 12V
Calculate the
current flowing through the resistors
voltage across the resistors
power dissipation in the resistors
Solution 19.1 . . . Series Circuit
R1 = 3Ω
R2 = 6Ω
V = 12V
Req = 9Ω
V = 12V
Req = R1 + R2
I = 12/9 =4/3 A
V1 = 4/3 x 3 = 4 V
V2 = 4/3 x 6 = 8 V
Example 19.2 . . . Parallel Circuit
R1 =6 Ω
R2 = 3 Ω
12V
Calculate the
current flowing through the resistors
voltage across the resistors
power dissipation in the resistors
Example 19.2 . . . Parallel Circuit
R1 =6 Ω
Req =2Ω
R2 = 3 Ω
12V
V = 12V
1/ Req = 1/R1 + 1/R2
I1 = 12/6 =2 A
I2 = 12/3 =4 A
Example 19.3 . . . Series /Parallel Combo Special!
R2 =6Ω
R3 =4Ω
R1 =3Ω
V =12V
Calculate the
current flowing through the resistors
voltage across the resistors
power dissipation in the resistors
Solution 19.3 . . . Series /Parallel Combo Special!
R2 =6Ω
R3 =4Ω
Req =2Ω
R3 =4Ω
R1 =3Ω
V =12V
Ieq = 12/6 =2A
Veq = 2 x2 = 4V
V1 = V2 = 4V
I1 = 4/3 A and I2 = 2/3 A
V =12V
Ammeters and Voltmeters
V
A
Voltmeter measures voltage
Ammeter measures current
Voltmeter is connected in parallel
Ammeter is connected in series
Voltmeter has a HIGH resistance
Ammeter has a LOW resistance
Voltmeter is easy to hook up
Ammeter is tricky to hook up
Capacitors in Parallel
C1 =6  F
C2 = 3  F
12V
Ceq = C1 + C2
V1 = V 2
Q1 and Q2 may be different
Capacitors in Series
C1 = 3  F
C2 = 6  F
V = 12V
1/Ceq = 1/C1 + 1/C2
Q1 = Q2
V1 and V2 may be different
RC Charging Circuit
V0
VR
VC
VC = V0 (1 - e -t /RC )
VR = V0 e -t /RC
t
RC Discharging Circuit
VR =VC
VC = V0 e -t /RC
VR = V0 e -t /RC
t
That’s all folks!