Download Equivalent Resistance

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.
10 Ω
9V
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)
3Ω
5V
5Ω
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)
6Ω
12V
2Ω
Using Ohm’s Law (V=IR)
• Ohm’s Law can be applied to
A) the WHOLE circuit
or
B) each RESISTOR separately
Ohm’s Law- WHOLE Circuit
• What is Rtotal for the circuit? What is the
current?
3Ω
5V
5Ω
Ohm’s Law- WHOLE Circuit
• Rtotal: Rtotal  R1  R2  3  5  8
• I:
V  IR  5V  I (8)
5V
I
 0.6 A
8
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• What is the voltage in each resistor?
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• What do we know about the current in each
resistor?
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• What do we know about the current in each
resistor?
Itotal  I1  I 2
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.
3Ω resistor
5Ωresistor
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.
3Ω resistor
5Ωresistor
V  IR
V  (0.6 A)(3)
V  1.8V
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• With that in mind we can solve for voltage.
3Ω resistor
5Ωresistor
V  IR
V  (0.6 A)(3)
V  IR
V  (0.6 A)(5)
V  1.8V
V  3.0V
3Ω
5V
5Ω
Ohm’s Law- EACH Resistor
• Double check your answer to be sure.
3Ω resistor
5Ωresistor
V  IR
V  (0.6 A)(3)
V  IR
V  (0.6 A)(5)
V  1.8V
V  3.0V
3Ω
1.8V  3.0V  5V
5Ω
Summary- SERIES Circuits
• We can write the ways we used Ohm’s Law as:
Whole
Circuit
Resistor 1, Resistor 2, Resistor3, …
Vtotal  V1  V2  V3  ...
I total  I1  I 2  I 3  ...
Rtotal  R1  R2  R3  ...
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
2Ω
10V
4Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE
circuit:
1
1 1
1
1
 


Rtotal R1 R2 2 4
V=10V
1
 0.75
Rtotal
1
Rtotal 
 1.33
.75
2Ω
10V
4Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE
circuit:
V=10V
Rtotal=1.33Ω
I=?
2Ω
10V
4Ω
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)
2Ω
10V
4Ω
PARALLEL (WHOLE circuit)
• To apply Ohm’s Law (V=IR) to the WHOLE
circuit:
V=10V
Rtotal=1.33Ω
I=7.51A
2Ω
10V
4Ω
PARALLEL (EACH resistor)
• Now find the CURRENT in each resistor.
2Ω
10V
4Ω
PARALLEL (EACH resistor)
• What do we know about VOLTAGE in a
PARALLEL circuit?
2Ω
10V
4Ω
PARALLEL (EACH resistor)
• The VOLTAGE is the same everywhere…
V= 10Volts everywhere…
2Ω
10V
4Ω
PARALLEL (EACH resistor)
• Now use V=IR to solve for current at each
resistor:
2Ω resistor
4Ω resistor
V  IR
10V  I (2)
V  IR
10V  I (4)
5A  I
2.5 A  I
2Ω
V= 10V
10V
4Ω
V= 10V
PARALLEL (EACH resistor)
Total Circuit: V=10V Rtotal=1.33Ω
I=7.51A
Compare the currents
Equal
2Ω resistor
4Ω resistor
V  IR
10V  I (4)
V  IR
10V  I (2)
+
5A  I
2.5 A  I
2Ω
V= 10V
10V
4Ω
V= 10V
Summary of Ohm’s Law
• For PARALLEL circuits:
• Vtotal=V1=V2=V3=…
• Itotal=I1+I2+I3+…
2Ω
10V
1
1
1
1
 
  ...
•
Rtotal R1 R2 R3
4Ω
Practice
• Find
• A) total resistance in circuit
• B) current in each resistor
6Ω
12V
2Ω