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DC Circuits
AP Physics
Chapter 18
DC Circuits
19.1 EMF and Terminal Voltage
The Electric Battery
EMF – electromotive force – the potential
difference between the terminals of a source
when no current flows to an external circuit (e)
19.1
The Electric Battery
A battery will have an internal resistance (r)
So there is a potential drop due to the current
that travels through the cell
Vc  Ir
So the actual potential across the terminals of
a cell will be
V  e  Ir
This is called the terminal
voltage
19.1
DC Circuits
19.2 Resistors in Series and in Parallel
Resistors in Series and in Parallel
When resistors are place in a single pathway
They are said to be in
series
A schematic would look
like this
19.2
Resistors in Series and in Parallel
The current in a series circuit is the same
throughout the circuit
IT  I1  I 2  ....I n
The potential across the source of EMF is
equal to the sum of the potential drops across
the resistors
VT  V1  V2  ....Vn
19.2
Resistors in Series and in Parallel
Since potential can be defined as
V  IR
We can rewrite the equation for potential as
I T ReqRVeqT I1V
R11 VIR22R2....
....
V
....
Rn nI n Rn
19.2
Resistors in Series and in Parallel
When resistors are place
in a multiple pathways
They are said to be in parallel
A schematic would look like this
19.2
Resistors in Series and in Parallel
The potential difference in a parallel circuit is
the same throughout the circuit
VT  V1  V2  ....Vn
The current through the source of EMF is
equal to the sum of the current through the
resistors
IT  I1  I 2  ....I n
19.2
Resistors in Series and in Parallel
Since current can be defined as
V
I
R
We can rewrite the equation for potential as
V1n
V1T V11 V12
IT  I1 I 2  ....I n
Req R1 R2
Rn
19.2
Resistors in Series and in Parallel
Circuits that contain both series and parallel
components need to be solved in pieces
This circuit contains
20W resistors in series
25W resistors and load series to each
other and parallel to the 40W
resistor
19.2
DC Circuits
19.3 Kirchoff’s Rules
Kirchoff’s Rules
Circuits that are a little more complex
We must use Kirchoff’s rules
Gustov Kirchoff
They are applications of the
laws of conservation of
energy and conservation
of charge
19.3
Kirchoff’s Rules
Junction Rule – conservation of charge
At any junction, the sum of the currents
entering the junction must equal the sum of all
the currents leaving the junction
I1  I 2  I 3
19.3
Kirchoff’s Rules
Loop Rule – the sum of the changes in
potential around any closed pathway of a
circuit must be zero
For loop 1
5V  5I1  2I 3  3V  0
19.3
Kirchoff’s Rules
Steps
I1
I3
I2
1. Label the current in each separate branch
with a different subscript (the direction does
not matter, if the direction is wrong, the
answer will have a negative value)
2. Identify the unknowns and apply V=IR
3. Apply the junction rule (at a in our case) so
that each current is in at least one equation
I1  I 2  I 3  0
19.3
Kirchoff’s Rules
Steps
I1
I3
I2
4. Choose a loop direction (clockwise or
counterclockwise)
5. Apply the loop rule (again enough equations
to include all the currents)
a. For a resistor apply Ohm’s law – the value
is negative if it goes in the direction of the
current
b. For a battery, the value is positive if the
loop goes from – to + (nub to big end)
19.3
Kirchoff’s Rules
Steps
I1
I3
I2
We’ll do the two inside loops
E1  I1R1  I 3R4  E3  I1R2  0
E3  I 3 R4  I 2R3  E2  0
6. Combine the equations and solve
19.3
DC Circuits
19.5 Circuits Containing Capacitors in Series and
in Parallel
Circuits Containing Capacitors
For a parallel set of
capacitors – the total
charge is the sum of
the individual charges
QT  Q1  Q2  ..Qn
In all parallel circuits – the potential across
each branch is the same as the total
VT  V1  V2  ..Vn
19.5
Circuits Containing Capacitors
The equivalent capacitance is the value of one
capacitor that could replace all those in the
circuit with no change in charge or potential
Since
Q  Q  Q  ..Q
T
And
We combine and get
1
2
n
Q  CV
CeqVC

C1C
V1  C2V2 ..C..nCnVn
T eq
19.5
Circuits Containing Capacitors
Series capacitors
The magnitude of the charges is the same on
each plate
QT  Q1  Q2  ..Qn
19.5
Circuits Containing Capacitors
The total potential is the sum of the potential
drops across each capacitor
VT  V1  V2  ..Vn
We then use that equation and the equation
for capacitance
Q
V
We get
C
Q
Q1T Q
11 Q
12
1n
 
 ..
Ceq C1 C22
Cnn
19.5
DC Circuits
19.6 RC Circuits-Resistors and Capacitors in
Series
RC Circuits
Used
windshield wipers
timing of traffic lights
camera flashes
19.5