Download + – Series Circuits - Eleanor Roosevelt High School

Lesson 19
Electric Circuits
Eleanor Roosevelt High School
Chin-Sung Lin
Electric Circuits
• Any path along which electrons can flow is
a circuit
• Complete circuit with no gaps
• A gap/break in electric circuit results in a
complete stop in the flow of electricity
Electric Circuits
Electric Circuits
Electric Circuits
• The components are commonly connected
in one of the two ways, series or parallel
Series Circuits
• When connected in series, they form a
single pathway for current to flow
Series Circuits
• Draw the schematic diagram
Series Circuits
• Schematic diagram
Parallel Circuits
• When connected in parallel, they form
branches
• Each branch is a separate path for current
Parallel Circuits
• Draw the schematic diagram
Parallel Circuits
• Schematic diagram
Series Circuits
Series Circuits
• Label the circuit
Series Circuits
• Label the circuit
+ V1 –
R1
R2
+ V2 –
I1
I
+ V
–
I2
Series Circuits
• Electric current has a single pathway, so the
current passing through each electronic
device is the same
+ V1 –
R1
R2
+ V2 –
I1
I
+ V
–
I2
I = I1 = I2
Series Circuits
• Water flow model of series circuits
Series Circuits
• The total voltage is the sum of individual
voltage drops along the circuit path
V = V 1 + V2
+ V1 –
R1
R2
+ V2 –
I1
I
+ V
–
I2
Series Circuits
V = V1 + V2
V = IR (Ohm’s Law applied to each device)
IReq = I1R1 + I2R2
since I = I1 = I2
Req = R1 + R2
Series Circuits
• The total resistance is the sum of individual
resistances along the circuit path
Req = R1 + R2
+ V1 –
R1
R2
+ V2 –
I1
I
+ V
–
I2
Series Circuits
• The current in the circuit is numerically
equal to the voltages supplied by the source
divided by the total resistance of the circuit
(Ohm’s law)
V = I Req = I (R1 + R2)
I = V / Req =V / (R1 + R2)
Series Circuits
• What will happen to the resistance if the
number of devices increases?
Series Circuits
• What will happen to the resistance if the
number of devices increases?
As the number of devices increases, the overall
resistance of the circuit is increased
Series Circuits
• Why is the overall resistance of the circuit
increased as the number of devices
increases?
R1
+
V1
–
R2
+
V2 –
I1
I2
I
R3
+
V
+
–
V3 –
I3
R4
+
V4 –
I4
Series Circuits
• Why is the overall resistance of the circuit
increased as the number of devices
increases?
Voltage drop for the device decreases, the total
current is decreased, resistance is increased
R1
+
V1
–
R2
+
V2 –
I1
I2
I
R3
+
V
+
–
V3 –
I3
R4
+
V4 –
I4
Series Circuits
• The overall resistance of the circuit is higher
than any resistance of the existing devices
Series Circuits
• The amount of power consumed by the
entire circuit is equal to the sum of the
power consumed by each device
V = V1 + V2
and
I = I1 = I2
IV = I1V1 + I2V2
since P = IV (applied to each device)
P = P1 + P2
Series Circuits
Series Circuits
I = I1 = I2
V = V 1 + V2
Req = R1 + R2
P = P1 + P2
Series Circuits Exercise
• Three 3-Ω resistors placed in series would
provide a resistance which is equivalent to
one _____Ω- resistor
• Three resistors with resistance values of 2-Ω
, 4-Ω , and 6-Ω are placed in series. These
would provide a resistance which is
equivalent to one _____Ω- resistor
Series Circuits Exercise
• As the number of resistors in a series circuit
increases, the overall resistance __________
and the current in the circuit __________
• Three identical light bulbs are connected in
series and connected to a battery. Compare
the brightness of them
Series Circuits Exercise
• A circuit has one resistor and the current is
4 A. If we add another identical resistor into
the circuit in series, the current will
become _________ A
• A circuit has one resistor and the current is
4 A. If we add another 3 identical resistors
into the circuit in series, the current will
become _________ A
Series Circuits Exercise
• Calculate the total resistance R and total
current I
300 Ω
200 Ω
4.5 V
I
Series Circuits Exercise
• Calculate the equivalent resistance and
voltage V of the cell
40 Ω
80 Ω
V
0.1 A
Series Circuits Exercise
• Calculate the resistance R
300 Ω
R
3V
0.002 A
Series Circuits Exercise
• If the voltage drop for the 10 Ω resistor is 2
V, calculate the total current I and the
voltage V of the cell
10 Ω
40 Ω
+ 2V –
V
I
Series Circuits Exercise
• Calculate and compare V1 and V2
10 Ω
40 Ω
+ V1 –
+ V2 –
10 V
Series Circuits Exercise
• Calculate the Power P1, P2, and total power P
of the circuit
10 Ω
40 Ω
P1
P2
10 V
Series Circuits Exercise
• Calculate all the unknown quantities in the
diagram
+ V1 –
200 Ω
+ V2 –
400 Ω
I1
I
+ 3V –
I2
Series Circuits
• What will happen to the circuit if we add a
wire to the circuit?
Series Circuits
• What is the disadvantage of the series
circuits?
Series Circuits
• What is the disadvantage of the series
circuits?
If one device fails, current in whole circuit
ceases and none of the devices will work
When more devices added, the total current
reduced
Parallel Circuits
Parallel Circuits
• Label the circuit
Parallel Circuits
• Label the circuit
+ V1 –
I1
+ V2 –
I2
R1
R2
I
+ V
–
Parallel Circuits
• Each device connected to the same two
points of the circuit. The voltage is the same
across each device
+ V1 –
I1
+ V2 –
I2
R1
R2
I
+ V –
V = V 1 = V2
Parallel Circuits
• Water flow model of parallel circuits
Parallel Circuits
• The total current in the circuit equals the
sum of currents in its parallel branches
+ V1 –
I1
+ V2 –
I2
R1
R2
I
+ V –
I = I1 + I2
Parallel Circuits
I = I1 + I2
I = V/R (Ohm’s Law applied to each device)
V/Req = V1 / R1 + V2 / R2
Since V = V1 = V2
1 /Req = 1 / R1 + 1 / R2
Req = R1 R2 / (R1 + R2 )
or
Parallel Circuits
• The reciprocal of total resistance is the sum of
reciprocals of individual resistances in the circuit
+ V1 –
R1
R2
I
+ V2 –
+ V –
1 / Req = 1 / R1 + 1 / R2
I1
I2
Parallel Circuits
• The current in the circuit is numerically
equal to the voltages supplied by the source
divided by the total resistance of the circuit
(Ohm’s law)
V = I Req = I R1 R2 / (R1 + R2)
I = V / Req =V (R1 + R2) / R1 R2
Parallel Circuits
• What will happen to the resistance if the
number of parallel branches increases?
Parallel Circuits
• What will happen to the resistance if the
number of parallel branches increases?
As the number of parallel branches increase,
the overall resistance of the circuit is
decreased
Parallel Circuits
• Why is the overall
resistance of the
circuit decreased as
the number of
parallel branches
increases?
R1
R2
R3
R4
I
+ V1 –
I1
+ V2 –
I2
+ V3 –
I3
+ V4 –
I4
+ V –
Parallel Circuits
• Why is the overall
resistance of the
circuit decreased as
the number of
parallel branches
increases?
R1
R2
R3
R4
Total current is
increased, resistance is
decreased
I
+ V1 –
I1
+ V2 –
I2
+ V3 –
I3
+ V4 –
I4
+ V –
Parallel Circuits
• The overall resistance of the circuit is
lowered than any resistance of the added
branches
Parallel Circuits
• The amount of power consumed by the
entire circuit is equal to the sum of the
power consumed by each device
V = V1 = V2
and
I = I1 + I2
IV = I1V1 + I2V2
since P = IV (applied to each device)
P = P1 + P2
Parallel Circuits
Parallel Circuits
I = I1 + I2
V = V1 = V2
1/Req = 1/R1 + 1/R2
Req = R1 R2 / (R1 + R2 )
P = P1 + P2
or
Parallel Circuits Exercise
• Three 3-Ω resistors placed in parallel would
provide a resistance which is equivalent to
one _____Ω- resistor
• Two resistors with resistance values of 20-Ω
and 40-Ω are placed in parallel. These
would provide a resistance which is
equivalent to one _____Ω- resistor
Parallel Circuits Exercise
• As more and more resistors are added in
parallel to a circuit, the equivalent
resistance of the circuit ____________ and
the total current of the circuit
____________
• Three identical light bulbs are connected in
parallel and connected to a battery.
Compare the brightness of them
Parallel Circuits Exercise
• A circuit has one resistor and the current is
2 A. If we add another identical resistor into
the circuit in parallel, the total current will
become _________ A
• A circuit has one resistor and the current is
2 A. If we add another 3 identical resistors
into the circuit in parallel, the current will
become _________ A
Parallel Circuits Exercise
• Calculate the total resistance R and total
current I
10 Ω
20 Ω
I
+ 3.0 V –
Parallel Circuits Exercise
• Calculate and compare I1 and I2
I
10 Ω
I1
40 Ω
I2
+ 10 V –
Parallel Circuits Exercise
• Calculate the equivalent resistance and
voltage V of the cell
40 Ω
80 Ω
0.1 A
+ V –
Parallel Circuits Exercise
• Calculate the resistance R
300 Ω
R
0.2 A
+ 3.0 V –
Parallel Circuits Exercise
• If the current for the 10 Ω resistor is 2 A,
calculate the voltage V of the cell and the
10 Ω
2A
total current I
40 Ω
I
+ V –
Parallel Circuits Exercise
• Calculate the Power P1, P2, and total power P
of the circuit
10 Ω
40 Ω
I
P1
P2
+ 10 V –
Parallel Circuits Exercise
• Calculate all the unknown quantities in the
diagram
200 Ω
400 Ω
I
+ V1 –
I1
+ V2 –
I2
+ 3V –
Parallel Circuits
• What will happen to the circuit if we cut a
wire of the circuit?
Parallel Circuits
• What is the disadvantage of the parallel
circuits?
Parallel Circuits
• What is the disadvantage of the parallel
circuits?
When more branches are added, a greater
amount of total current occurs in the line
and can be over its safe amount – overload
Sometimes, it requires more wires
Compound Circuits
Equivalent Resistance
• The value of a single resistor that would
comprise the same load of several resistors
in its network to the battery or power source
Equivalent Resistance of
Series Circuits
• What’s the equivalent resistance?
R1
+
V1
–
R2
+
V2 –
I1
I2
I
R3
+
V
+
–
V3 –
I3
Rn
+
Vn –
In
Equivalent Resistance of
Series Circuits
• What’s the equivalent resistance?
Req = R1 + R2 + R3+ …… + Rn
R1
+
V1
–
R2
+
V2 –
I1
I2
I
R3
+
V
+
–
V3 –
I3
Rn
+
Vn –
In
Equivalent Resistance of
Series Circuits
• What’s the equivalent resistance?
V1 –
I1
V
R2 + 2 –
I2
V3 –
I3
R1 +
R3 +
………
Rn
I
+ Vn –
+ V –
In
Equivalent Resistance of
Series Circuits
• What’s the equivalent resistance?
V1 –
I1
V
R2 + 2 –
I2
V3 –
I3
R1 +
1/Req = 1/R1 + 1/R2
+ …… + 1/Rn
R3 +
………
Rn
I
+ Vn –
+ V –
In
Compound Circuits
• The equivalent resistor of a compound
circuit can be found by combining resistors
in series and in parallel
Compound Circuits
R1
R3
R2
R 1-2
R3
R 1-2-3
Compound Circuits
• The equivalent resistor of a compound
circuit can be found by combining resistors
in series and in parallel
Compound Circuits
R2
R1
R3
R 1-2
R3
R 1-2-3
Compound Circuits Example
• Calculate the equivalent resistance of the
following compound circuit
2Ω
3Ω
2Ω
Compound Circuits Example
• Calculate the equivalent resistance of the
following compound circuit
R1 = 2 Ω
R1-2 = R1R2 /(R1+R2)
R1-2 = 22/(2+2) Ω= 1 Ω
R1-2-3 = R1-2 +R3
R1-2-3 = 1 Ω + 3 Ω = 4 Ω
R2 = 2 Ω
R3 = 3 Ω
Compound Circuits Example
• Calculate the equivalent resistance R and
the total current I
2Ω
1Ω
4Ω
7V
Compound Circuits Example
• Calculate the equivalent resistance R and
the total current I
R1-2 = R1R2 /(R1+R2)
R1-2 = 24/(2+4) Ω= 4/3 Ω
R = R1-2 +R3
R = 4/3 Ω + 1 Ω = 7/3 Ω
I = V/R
= 7 V / (7/3 Ω)
=3A
R1 = 2 Ω
R3 = 1 Ω
R2 = 4 Ω
7V
Compound Circuits Exercise
• Calculate the equivalent resistance R and
the total current I
10 Ω
20 Ω
15 Ω
30 Ω
12 V
Compound Circuits Exercise
• Calculate the the total current I and total
voltage V
0.1 A 10 Ω
20 Ω
15 Ω
30 Ω
I
V
Compound Circuits Exercise
• If R1 = R2, calculate the R1, I2 , and the total
current I
R1
I2
R2
+ 10 V –
+ 4V –
40 Ω
Electric Circuits
Electric Circuit Symbols