Download R - IBPhysicsLund

NOTE: If instead of a two lane highway you had a three lane highway,
a roadblock in one lane would slow the traffic by about a third.
Topic 5.2 Extended
A – Resistances in series and parallel
The easiest way to picture a resistor is as a road
construction
zone
in would
a highway:
A roadblock in two
lanes
slow the traffic by about two thirds.
Here is the highway, supporting the maximum traffic
FYI: The roadblocks are one after the other, AKA INLINE. We say that
flow.
they are in series.
Here is the construction zone, constricting the flow
of traffic:
Of course, what will really happen is that the blocked
lane of traffic will merge with the moving one.
Cutting the speed by about a factor of two.
FYI: The roadblocks are in parallel.
Topic 5.2 Extended
A – Resistances in series and parallel
Now imagine two parallel two-lane highways:
Each highway begins by supporting the original flow of
traffic from the previous slide.
Each highway has its traffic flow cut in half.
But there are TWO highways.
Thus the traffic flow is equivalent to a single
unblocked highway.
FYI: Combining two or more resistors is series produces a resistance
that is larger than any single resistor.
Topic 5.2 Extended
FYI: Combining two or more resistors is parallel produces a resistance
A – Resistances in series and parallel
that is smaller than any single resistor.
We can think of resistances in series in another way:
Placing resistors in series increases the EFFECTIVE
LENGTH of the resistor.
L
L
L
SERIES
RL
3L
Placing resistors in parallel increases the EFFECTIVE
AREA of the resistor.
A
A
A
3A
PARALLEL
R1/A
Topic 5.2 Extended
A – Resistances in series and parallel
Now for some formulas...
Consider three resistors in SERIES, as shown:
Note that the
V
current I is the
+
same everywhere.
Recall that the
sum of the
R2
R3
R1
voltages in a
loop equals the
terminal voltage
of the battery:
V1
V2
V3
Thus
V = V1 + V2 + V3
= IR1 + IR2 + IR3
= I(R1 + R2 + R3)
= IRs where Rs is the equivalent series resistance.
SERIES
Rs = R1 + R2 + R3
Equivalent Series
Resistance Rs
Topic 5.2 Extended
A – Resistances in series and parallel
Consider three resistors in PARALLEL, as shown:
Note that the voltage V is
1
+
R1
1
1
+
R2
R3
I2
I1
A1
V
-
1
=
Rp
Ap
I
I3
A3
A2
+
the same everywhere.
V = V1 = V2 = V3
Because of the conservation
of charge, the sum of the
currents going through the
resistors must equal the
total current:
I = I1 + I2 + I3
From Ohm's law,
V2
V1
V
V
=
+
+ 3
R2
R1
R3
Rp
V
V
V
V
=
+
+
R2
R1
R3
Rp
R1
R2
PARALLEL
Equivalent Parallel
Resistance Rp
R3
Topic 5.2 Extended
A – Resistances in series and parallel
Find the equivalent resistance (from A to B) of the
following resistor setup:
A
25 
50 
100 
B
The resistors are in SERIES so that
Rs = R1 + R2 + R3
Rs = 25 + 50 + 100
Rs = 175 
Topic 5.2 Extended
A – Resistances in series and parallel
1
1
1
1
=
+
+
25
50
100
Rp
4
2
1
1
=
+
+
100
100
100
Rp
7
1
=
100
Rp
Rp = 14.28 
B
100 
25 
The resistors are in
PARALLEL so that
1
1
1
1
=
+
+
R2
R1
R3
Rp
A
50 
Find the equivalent
resistance of the
following resistor
setup:
Topic 5.2 Extended
A – Resistances in series and parallel
The resistors are in SERIES:
Rs = R1 + R2
B
A
50 
REDUCED
FORM
Rs = 50 + 20
Rs = 70 
100 
50 
B
20 
Two resistors are in
PARALLEL so that
1
1
1
=
+
R2
R1
Rp
1
1 4
1
=
+
100
25 4
Rp
5
1
=
Rp = 20 
100
Rp
A
25 
Find the equivalent resistance of the following
resistor setup:
Topic 5.2 Extended
A – Resistances in series and parallel
The current through the circuit with three resistors
in SERIES...
...will stop if
any one resistor
is removed.
-
+
The current through the
Ap
A1
+
circuit with three
resistors in PARALLEL...
Will NOT stop if
any one resistor
is removed.
A2
A3
-