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Resistors in Series
• All the current must follow the same path.
• Each component has the same current going
through it
•
If current is disrupted through one element (e.g. the light goes out)
then they all go out.
Resistors in Series
• All the current must follow the same path.
• Each component has the same current going
through it
•
If current is disrupted through one element (e.g. the light goes out)
then they all go out.
Equivalent or total or effective resistance is the one that
could replace all resistors resulting in the same current.
Req = R1+ R2 + R3
Adding more resistors in series increases equivalent
resistance!
Resistors in Parallel
•
Current can branch to multiple paths
• Current varies through each resistor (greater
resistance = smaller current).
• The current flowing into a node equals the
current that flows out of that node
I = I1 + I2 + I3 .
• The voltage drop across each resistor is the
same.
•
Each device is independent; if one resistor goes out, the others keep
working.
Resistors in Parallel
•
Current can branch to multiple paths
• Current varies through each resistor (greater
resistance = smaller current).
• The current flowing into a node equals the
current that flows out of that node
I = I1 + I2 + I3 .
• The voltage drop across each resistor is the
same.
•
Each device is independent; if one resistor goes out, the others keep
working.
1
1
1
1
=
+
+
Req R1 R2 R3
equivalent resistance
is smaller than the
smallest resistance.
We do: Calculating Req
We do: Calculating Req
Req = R1 + R2 = 8 Ω + 8 Ω = 16 Ω
1
𝑅𝑒𝑞
=
1
𝑅1
+
Req = 4 Ω
1
𝑅2
=
1
8Ω
+
1
8Ω
=
1
4Ω
We do: Calculating Req
We do: Calculating Req
You do: Calculating Req
You do: Calculating Req
Calculating Current, Potential Drop, and
Power Dissipated
• To calculate current through a circuit, find the Req for all resistors
in a circuit, then use Ohm’s Law (I = V/R)
Example: What is the current through this circuit?
Calculating Current, Potential Drop, and
Power Dissipated
• To calculate current through a circuit, find the Req for all resistors
in a circuit, then use Ohm’s Law (I = V/R)
Example: What is the current through this circuit?
I = 60V / 10Ω = 6A
RVIP tables
RVIP tables are to
help you organize
your information so
you can find current
through, voltage
drop across, or
power dissipated by
any resistor in a
circuit.
Click on me to
see a youtube
video on solving
this problem!
Resistor
R1
R2
R3
R4
Total
Resistance
(Ω)
Voltage Current
drop (V) (A)
Power
(W)
RVIP tables
Resistor Resistance Voltage Current
1) Simply the circuit
(Ω)
drop (V) (A)
so that it is consists of
only resistors in
R1
series.
R
Power
(W)
2
2) Find the total
resistance
R3
3) Find the total
voltage drop (that’s
the battery)
Total
4) Find the total
current through the
circuit
𝑉
(Use Itotal = 𝑡𝑜𝑡𝑎𝑙)
𝑅𝑡𝑜𝑡𝑎𝑙
5) Find the total
power dissipated
(Use Ptotal = VtotalItotal)
R4
16
24
1.5
36
RVIP tables
6) Record the
resistance of each
resistor in the
simplified diagram.
Resistor
R1
R2
R3
Only record the
R4
parallel resistors once
Total
in the table.
You can check your
work, because the
resistors should add
up to the total.
Resistance
(Ω)
Voltage Current
drop (V) (A)
Power
(W)
5
3
8
16
24
1.5
36
RVIP tables
7) Record the voltage
drop of each resistor,
using the total current
and the resistors in
the 2nd column.
Use V = IR
Only record the
voltage drop across
parallel resistors
once.
You can check your
work, because all the
voltage drops will
equal the total.
Resistor
R1
Resistance
(Ω)
Voltage Current
drop (V) (A)
5
7.5
3
4.5
R4
8
12
Total
16
24
R2
R3
1.5
Power
(W)
36
RVIP tables
7) Record the current
through each resistor.
Use the voltage drops
from column 3 and
the individual (not
equivalent)
resistances.
Use I =
𝑉
𝑅
You can check your
work because all
resistors in series
should be the same
as the total current,
and the current
through parallel
resistors should add
up to the total.
Resistor
R1
Resistance
(Ω)
Voltage Current
drop (V) (A)
5
7.5
1.5
3
4.5
1.1
0.4
R4
8
12
1.5
Total
16
24
1.5
R2
R3
Power
(W)
36
Notice: when current divides, most goes through
the path of least resistance!
RVIP tables
8) Find the power of
each resistor by
multiplying voltage
(column 3) with the
current (column 4).
Remember,
Power = VI
You can check your
work because the
power of each
resistor should add
up to the total power
(within rounding
error).
Resistor
Resistance
(Ω)
Voltage Current
drop (V) (A)
Power
(W)
5
7.5
1.5
11.3
1.1
0.4
5.0
3
4.5
R4
8
12
1.5
18
Total
16
24
1.5
36
R1
R2
R3
1.8
Example 2
Resistor
R1
R2
R3
R4
Total
Resistance
(Ω)
Voltage Current
drop (V) (A)
Power
(W)
Example 2
Resistor
R1
R2
Click on me for
a youtube video
on how to solve
this circuit!
Resistance
(Ω)
2
Voltage Current
drop (V) (A)
3
Power
(W)
1.5
4.5
1.0
3
0.5
1.5
2
3
R4
4
6
1.5
9
Total
8
12
1.5
18
R3
Example 3
Resistor
R1
R2
R3
Total
Resistance
(Ω)
Voltage Current
drop (V) (A)
Power
(W)
Example 3
Resistor
Resistance
(Ω)
Voltage Current
drop (V) (A)
R1
100
5
R2
67
3.4
R3
Total
167
9
Power
(W)
.05
0.25
.03
0.10
.02
0.07
.05
0.45
*Numbers slightly off totals due to rounding