Announcements Kirchhoﬀ’s Rules Combinations of Resistors Final Questions
DC Circuits
Sections 19.1  19.2
DC Circuits
Announcements
Kirchhoﬀ’s Rules Combinations of Resistors Final Questions
Reading Assignment
Read sections 19.3  19.4
Homework Assignment 3
Homework for Chapter 18 is due in class today
Homework Assignment 4
Homework for Chapter 19 (due at the beginning of class on Wednesday,September 22)
Q:1,4,7,19,22
P:2,8,26,32,38,52
DC Circuits
Announcements
Kirchhoﬀ’s Rules
Combinations of Resistors Final Questions
Kirchhoﬀ’s junction rule
At any
junction,the sum of the currents must equal zero
junction
I = 0
Currents directed into the junction are denoted as +I
Currents directed out of a junction are denoted as −I
In other words...
This rule simply states that for a steady ﬂow of charge,there is neither a buildup nor a depletion of charge at any
junction
DC Circuits
Announcements
Kirchhoﬀ’s Rules
Combinations of Resistors Final Questions
Kirchhoﬀ’s junction rule
At any
junction,the sum of the currents must equal zero
junction
I = 0
Currents directed into the junction are denoted as +I
Currents directed out of a junction are denoted as −I
In other words...
This rule simply states that for a steady ﬂow of charge,there is neither a buildup nor a depletion of charge at any
junction
Kirchhoﬀ’s loop rule
The sum of the potential diﬀerences across all circuit elements around any
closed circuit loop must be zero
closed loop
ΔV = 0
What does this mean?
Kirchhoﬀ’s loop rule is simply a statement of conservation of energy!
DC Circuits
Announcements
Kirchhoﬀ’s Rules
Combinations of Resistors Final Questions
Electromotive force
The electromotive force (emf) ε of a battery is the maximum possible voltage the battery can provide
between its terminals
Though its name implies that it is a force,emf is actually a potential diﬀerence (measured in volts)
Using Kirchhoﬀ’s rules
Label the current and the current direction in each branch (just guess a direction if you don’t know for sure)
Use Kirchhoﬀ’s junction rule to write down a current equation for each junction that gives you a diﬀerent
equation (every junction in the circuit except one)
Use Kirchhoﬀ’s loop rule to write down loop equations for as many loops as it takes to obtain,in
combination with the equations from the junction rule,as many equations as there are unknowns
Charges move from a highpotential to a lowpotential,so if a resistor is traversed in the direction
of the current,the potential diﬀerence is denoted as −IR
If the resistor is traversed in the direction opposite the current,the potential diﬀerence is denoted
as +IR
If a source of emf (with no internal resistance) is traversed in the direction of the emf (from
negative to positive),the potential diﬀerence is denoted as +ε
If a source of emf (with no internal resistance) is traversed in the direction opposite the emf (from
positive to negative),the potential diﬀerence is denoted as −ε
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Resistors
A resistor is an electronic component that impedes the ﬂow of electric current,converting some of its
energy into heat
When charge ﬂows through a resistor,it experiences a drop
in electric potential given by
ΔV = IR
The power delivered to the resistor by the current is
P = I ΔV = I
2
R =
(ΔV)
2
R
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Resistors
A resistor is an electronic component that impedes the ﬂow of electric current,converting some of its
energy into heat
When charge ﬂows through a resistor,it experiences a drop
in electric potential given by
ΔV = IR
The power delivered to the resistor by the current is
P = I ΔV = I
2
R =
(ΔV)
2
R
Internal resistance
Due to internal resistance in the battery,the actual potential diﬀerence between a battery’s terminals (the socalled
terminal voltage) is less than ε
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Series combination
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Series combination
The current through each resistor is the same (I
1
= I
2
= I ) (why?)
The total potential diﬀerence ΔV
tot
across resistors connected in series is the sum of the potential
diﬀerences across the individual resistors (ΔV
tot
= ΔV
1
+ ΔV
2
+...)
The equivalent resistance is the algebraic sum of the individual resistances
R
eq
= R
1
+ R
2
+ R
3
+...
Therefore,the equivalent resistance of a series combination of resistors is always greater than any
individual resistance
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Parallel combination
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Series combination
The current through each resistor is the same (I
1
= I
2
= I ) (why?)
The total potential diﬀerence ΔV
tot
across resistors connected in series is the sum of the potential
diﬀerences across the individual resistors (ΔV
tot
= ΔV
1
+ ΔV
2
+...)
The equivalent resistance is the algebraic sum of the individual resistances
R
eq
= R
1
+ R
2
+ R
3
+...
Therefore,the equivalent resistance of a series combination of resistors is always greater than any
individual resistance
Parallel combination
The potential diﬀerence across each resistor is the same (ΔV
1
= ΔV
2
= V) (why?)
The total current I is the sum of the currents across the individual resistors (I = I
1
+ I
2
+...)
The inverse of the equivalent resistance is the algebraic sum of the inverses of the individual resistances
1
R
eq
=
1
R
1
+
1
R
2
+
1
R
3
+...
Therefore,the equivalent resistance of a parallel combination of resistors is always less than the smallest
individual resistance in the group
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Scenario
Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Scenario
Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.
Question#1
If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Scenario
Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.
Question#1
If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?
Answer
It would go out
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Scenario
Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.
Question#1
If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?
Answer
It would go out
Question#2
If the ﬁlament of the second lightbulb fails,what would happen to the ﬁrst lightbulb?
DC Circuits
Announcements Kirchhoﬀ’s Rules
Combinations of Resistors
Final Questions
Scenario
Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.
Question#1
If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?
Answer
It would go out
Question#2
If the ﬁlament of the second lightbulb fails,what would happen to the ﬁrst lightbulb?
Answer
It would go out
DC Circuits
Announcements Kirchhoﬀ’s Rules Combinations of Resistors
Final Questions
Reading Assignment
Read sections 19.3  19.4
Homework Assignment 3
Homework for Chapter 18 is due in class today
Homework Assignment 4
Homework for Chapter 19 (due at the beginning of class on Wednesday,September 22)
Q:1,4,7,19,22
P:2,8,26,32,38,52
DC Circuits
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