Lecture 11
Chapter 31
Physics II
Resistors
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
95.144
Lecture Capture:
http://echo360.uml.edu/danylov201415/physics2spring.html
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Circuit Elements
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Slide 31-22
Resistors
in series/parallel
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Resistors in Parallel
Real circuit
I2
I3
We have replaced 3 resistors
with a “equivalent” resistor.
ΔV
I
 Resistors in parallel have
the same potential difference, ΔV
Equivalent circuit
I1
Consider three resistors connected in parallel.
ΔV
Req is inserted without changing the
operation of the circuit, so I and ΔV
are same as in the real circuit
=
Conservation of current I
Ohm’s law
+ +
;
;
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
+ +
+ + Equivalent resistance of resistors in parallel.
Resistors in Series
ΔV2
ΔV1
ΔV3
ΔV
Equivalent circuit
Real circuit
Consider three resistors connected in series.
ΔV
Req is inserted without changing the
operation of the circuit, so I and ΔV
are same as in the real circuit
+
+
Ohm’s law ∆
∆
∆
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
+
+
+
+
Equivalent resistance of resistors in series.
ConcepTest 1 Headlights

Are headlight wired:
A) in parallel?
B) in series?
ConcepTest 2

Resistors I
The battery current I is
A) 3 A
B) 2 A
C) 1 A
D) 2/3 A
E) ½ A
+
=2/3 A
ConcepTest 3

Resistors II
The battery current I is
A) 3 A
B) 2 A
C) 1 A
D) 2/3 A
E) ½ A
+ =4
=3 A
Example:
Analyzing a complex circuit
a)Find the equivalent resistance.
b)Find the current through and
the potential difference across
each of the resistors in the circuit.
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Real batteries
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Real Batteries. Internal resistance
To drive a current in a circuit we need a “charge pump”, a device that by
doing work on the charge carriers maintains a potential difference.
Let’s look at a gravitational analog of a battery:
Give me a
break! I do it
as fast as I
can!
∆
Terminal voltage
A person does work to maintain a steady flow of balls through “the circuit”.
However, this guy cannot move balls instantaneously. It takes time.
So there is a natural hindrance to a completely free flow.
To describe this hindrance we can introduce the internal resistance, r.
It is inside a battery and it cannot be separated from the battery.
ε
(EMF, )
Pot. difference of a battery without an internal resistance is called an electromotive force.
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Why is electric energy useful?
It can be easily transformed into other forms of energy.
Mechanical
energy
Thermal
energy
Electric energy
E/M waves
How to find the power transformed by these electrical devices
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Light
Electric Power
Consider any electrical device:
Δt (for Q to go through the device)
Some charge Q
ΔV
As some charge Q moves through the potential difference ΔV, the potential energy
of the charge changes by: ∆
∆
Let Δt be the time required the charge to move through the potential difference ΔV.
Then, the power P (the rate energy is transformed, Physics I) is:
∆
∆
∙∆
∆
∆
∙∆
∙∆
The power transformed by a resistor can be written like this: 95.144 Danylov Lecture 11
Department of Physics and Applied Physics
∙∆
∆
power transformed by an electrical device
∙
∆ /
ConcepTest 5
Electric Power
Most loudspeakers are designed to have a
resistance of 4 Ω. If it is connected to an
amplifier with a rating of 100 W, what is
the current to the loudspeaker?
A) 2 A
B) 3 A
C) 4 A
D) 5 A
E) 25 A
∙∆
∆
∙
What you should read
Chapter 31 (Knight)
Sections






31.1
31.3
31.4
31.5
31.6
31.7 (Example 31.29)
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
Thank you
See you
95.144 Danylov Lecture 11
Department of Physics and Applied Physics
ConcepTest 4
Series Resistors I
Assume that the voltage of the battery is 9 V
and that the three resistors are identical.
What is the potential difference across each
resistor?
A) 12 V
B) zero
C) 3 V
D) 4 V
E) you need to know the
actual value of R
Since the resistors are all equal,
R
R
R
the voltage will drop evenly
across the 3 resistors, with 1/3 of
9 V across each one. So we get a
3 V drop across each.
9V