Lecture 11
Chapter 31
Physics II
02.27.2015
Resistor
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
95.144
Lecture Capture:
http://echo360.uml.edu/danylov201415/physics2spring.html
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Circuit Elements
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Slide 31-22
Resistors in Parallel
Real circuit
I2
I3
We have replaced 3 capacitors
with a “equivalent” capacitor.
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, Spring 2015, 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, Spring 2015, Lecture 11
Department of Physics and Applied Physics
+
+
+
+
Equivalent resistance of resistors in series.
Series resistors
The current I is the same through all resistors placed in series.
Parallel resistors
The potential differences V are the same across all resistors placed in parallel
=
The behavior of the circuit will be unchanged if the N parallel/series
resistors are replaced by the single resistor Req
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
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
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
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, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Kirchhoff’s Law
Some circuits are too complicated to analyze
(none of the elements are in series/parallel)
Kirchhoff’s rules are very helpful.
To analyze a circuit means to find:
1. ΔV across each component
2. The current in each component
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Kirchhoff’s Junction Law
For a junction, the law of conservation of current requires that:
3
out
2
1
in
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Kirchhoff’s Loop Law
For any path that starts and ends at the same point:
The sum of all the potential differences encountered
while moving around a loop or closed path is zero.
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
ConcepTest 5
Junction Rule
A) 2 A
What is the current in branch P?
B) 3 A
C) 5 A
D) 6 A
E) 10 A
The current entering the junction
5A
in red is 8 A, so the current
leaving must also be 8 A. One
P
8A
exiting branch has 2 A, so the
other branch (at P) must have 6 A.
Junction
2A
6A
What you should read
Chapter 31 (Knight)
Sections




31.1
31.4
31.6
31.7 (Example 31.29)
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics
Thank you
See you on Tuesday
95.144, Spring 2015, Lecture 11
Department of Physics and Applied Physics