PHYS105
Module 7- Resistors
I.
Combining Resistors in Parallel and Series
A.
Series –
Placing resistors in series makes a ___________________________ resistor.
R1
R2
Analogous to making the length __________________!!!
R1
R2
Req
B.
Parallel Placing resistors in parallel creates a _______________________ resistor.
R1
R2
Analogous to making the area __________________!!!
R1
R2
R3
Req
B.
Special Cases - Short Cuts
1.
For TWO resistors in parallel, we have
2.
For N identical resistors in parallel, we have
EXAMPLE 1: What is the resistance between the terminals A and D in the following
circuit?
B
A
2 kΩ
4 kΩ
1 kΩ
D
C
4 kΩ
SOLUTION:
The two 4 kΩ resistors are in __________________________________. Thus, we have
These three resistors are now in _____________________________. Thus, we have
RESULT:
EXAMPLE 2: What is the resistance between terminals A and B in the following
circuit?
A
6 kΩ
B
SOLUTION:
4 kΩ
EXAMPLE 3: What is the resistance between terminals A and B in the following
circuit?
A
9 kΩ
B
SOLUTION:
9 kΩ
9 kΩ
II.
Short and Open Circuits
A.
Definition of a Short Circuit:
A short circuit is when __________ ___________________ is dropped across a
circuit element.
B.
Special Case (Resistor):
For a resistive element, a short circuit also implies by ohm’s law that there is
________ _____________________.
EXAMPLE:
I=2A
+
R
V
-
V=IR
C.
Definition of an Open Circuit:
An open circuit is when ___________ _________________________ flows
through a circuit element.
D.
Special Case (Resistor):
For a resistive element, an open circuit also implies by ohm’s law that there is
_______________________ _____________________.
EXAMPLE:
I
+
VAB
A
B
V
I= AB
R
III.
Kirchhoff’s Laws:
Two fundamental physics conservation laws must be obeyed in all electric
circuits:
1)
Conservation of Energy
2)
Conservation of Charge
For a steady state circuit, these two laws were restated by Kirchhoff in terms of
voltage and current!!!
A.
Kirchhoff’s Voltage Law (KVL) – “Conservation of Energy”
The algebraic sum of the potential differences around any closed loop (closed
path) must equal _______________.
EXAMPLE: Write Kirchhoff’s voltage law for the following circuit.
B
C
R1
+
ε
R2
-
R3
A
D
B.
Kirchhoff’s Current Law (KCL) – “Conservation of Charge”
The algebraic sum of the currents at any point in the circuit must equal
____________________. In other words the sum of the currents entering a
junction must equal the ______________________________________________
.
EXAMPLE: Use Kirchhoff’s current law to find the current in resistor R2.
5 mA
4 mA
R1
R3
R2
I
IV.
Voltage and Current Divider Circuits
Knowledge of the voltage divider and current divider circuits can be extremely
useful both in designing and analyzing electronic circuits because:
A.
1)
They often allow us to use a single voltage or current supply to all the
necessary voltages and currents required;
2)
These circuits are so common that knowledge of their formulas can
greatly improve both our understanding and speed in analyzing electric
circuits.
Voltage Divider Circuit (Series)
I
C
A
R2
+
+
Vin
R1
V1
B
B.
Current Divider Circuit (Parallel)
I
I1
R1
R2
I2
V.
Battery or Power Supply – Source of EMF
A.
A battery is a _____________________ of ______________________
________________. It is a __________________ _________________
with its own energy supply.
B.
Schematic Symbol for Ideal Battery
B
A
+
ε
C
C.
Schematic Symbol for a Real Battery
A
B
Rint
+
ε
-
C
NOTE: We will see later that any circuit (no matter how complex) can be
reduced to a single voltage source in series with a resistor as long as we
generalize resistance to include complex numbers (called impedance). This is
known as the Thevinen’s equivalent circuit and is extremely powerful in solving
more complicated circuits and in design.
D.
Effect of Internal Resistance – Rint
In an electrical circuit, it is important for the internal resistance of a battery to be
much smaller than the load resistance connected to the battery. This is to ensure
that most of the energy is supplied to the load and not wasted as heat inside the
battery. The following example should demonstrate this point.
EXAMPLE: For a 13 volt battery with an internal resistance of 1 Ω, what voltage will
you measure at the batter terminals when a) the battery terminals are left open; b) a 12 Ω
resistor is connected between the terminals.
SOLUTION:
a)
1Ω
A
+
13 V
B
b)
1Ω
+
13 V
A
12 Ω
B