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Physics 223
28. Direct Current (DC) Circuits
28.1 EMF and Voltage
28.2 Resistors in Series and Parallel
28.3 Kirchhoff’s Rules
28.4 RC Circuit
28.5 Ammeters and Voltmeters
28.6 Household Wiring
Electric Battery
+
-
The battery converts chemical energy to
electrical energy. It is a source of potential
difference or voltage. This is used to drive
electrons “downhill” through a conductor
(resistor)
Electric Current and Ohm’s Law
I=Q/t
V=IR
current = charge / time
voltage = current x resistance
28.1 EMF and Voltage
V=
ɛ-Ir
r is the “hidden” internal resistance
of the battery.
28.2 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
Example 28.1 . . . 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 28.1 . . . 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 28.2 . . . 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
Solution 28.2 . . . 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 28.3 . . . 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 28.3 . . . 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
28.3 Kirchhoff’s Rules
 I = 0 (Junction)
 V = 0 (Loop)
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
28.5 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
That’s all folks!