Equivalent Resistance
Series and Parallel Circuits
Two Kinds of circuits
Circuit Diagrams
• When drawing pictures of circuits, symbols are used as shorthand instead of pictures of components.
Circuit Diagrams
• Instead of a battery, the symbol is used. (Note: sometimes voltage is called emf or
potential difference)
Circuit Diagrams
• Instead of a resistor, the symbol is used.
Circuit Diagrams
• Resistors and batteries will be labeled with their respective values most of the time.
9V
10 Ω
10 Ω
Practice
• Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω)
Practice
• Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω)
5V
3 Ω
5 Ω
Practice
• Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω)
Practice
• Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω)
12V
6 Ω 2 Ω
Using Ohm’s Law (V=IR)
• Ohm’s Law can be applied to
A) the WHOLE circuitor
B) each RESISTOR separately
Ohm’s Law- WHOLE Circuit
• What is Rtotal for the circuit? What is the current?
5V
3 Ω
5 Ω
Ohm’s Law- WHOLE Circuit
• Rtotal:
• I:
5V
3 Ω
5 Ω
85321 RRRtotal
AV
I
IVIRV
6.08
5
)8(5
Ohm’s Law- EACH Resistor
• What is the voltage in each resistor?
5V
3 Ω
5 Ω
Ohm’s Law- EACH Resistor
• What do we know about the current in each resistor?
5V
3 Ω
5 Ω
Ohm’s Law- EACH Resistor
• What do we know about the current in each resistor?
5V
3 Ω
5 Ω
21 IIItotal
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor
5V
3 Ω
5 Ω
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor
5V
3 Ω
5 Ω
VV
AV
IRV
8.1
)3)(6.0(
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.3Ω resistor 5Ωresistor
5V
3 Ω
5 Ω
VV
AV
IRV
8.1
)3)(6.0(
VV
AV
IRV
0.3
)5)(6.0(
Ohm’s Law- EACH Resistor
• Double check your answer to be sure.3Ω resistor 5Ωresistor
5V
3 Ω
5 Ω
VV
AV
IRV
8.1
)3)(6.0(
VV
AV
IRV
0.3
)5)(6.0(
VV 0.38.1
Summary- SERIES Circuits
• We can write the ways we used Ohm’s Law as:
...
...
...
321
321
321
RRRR
IIII
VVVV
total
total
total
Whole Resistor 1, Resistor 2, Resistor3, …Circuit
Practice
• Pg. 650 Practice A
Ohm’s Law for PARALLEL circuits
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE circuit:
V=10V
10V
2 Ω 4 Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE circuit:
V=10V
10V
2 Ω 4 Ω
33.175.
1
75.01
4
1
2
1111
21
total
total
total
R
R
RRR
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE circuit:
V=10V Rtotal=1.33Ω I=?
10V
2 Ω 4 Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE circuit:
V=10V Rtotal=1.33Ω I=?
V=IR → 10V=I(1.33Ω)
10V
2 Ω 4 Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE circuit:
V=10V Rtotal=1.33Ω I=7.51A
10V
2 Ω 4 Ω
PARALLEL (EACH resistor)
• Now find the CURRENT in each resistor.
10V
2 Ω 4 Ω
PARALLEL (EACH resistor)
• What do we know about VOLTAGE in a PARALLEL circuit?
10V
2 Ω 4 Ω
PARALLEL (EACH resistor)
• The VOLTAGE is the same everywhere…
10V
2 Ω 4 Ω
V= 10Volts everywhere…
PARALLEL (EACH resistor)
• Now use V=IR to solve for current at each resistor:
2Ω resistor 4Ω resistor
10V
2 Ω 4 ΩV= 10V V= 10V
IA
IV
IRV
5
)2(10
IA
IV
IRV
5.2
)4(10
PARALLEL (EACH resistor)
Total Circuit: V=10V Rtotal=1.33Ω I=7.51A
Compare the currents2Ω resistor 4Ω resistor
10V
2 Ω 4 ΩV= 10V V= 10V
IA
IV
IRV
5
)2(10
IA
IV
IRV
5.2
)4(10
Equal
+
Summary of Ohm’s Law
• For PARALLEL circuits:
• Vtotal=V1=V2=V3=…
• Itotal=I1+I2+I3+…
• ...1111
321
RRRRtotal
10V
2 Ω 4 Ω
Practice
• Find• A) total resistance in circuit• B) current in each resistor
12V
6 Ω 2 Ω
