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 ()
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
So the actual potential across the terminals of a cell will be
This is called the terminal
voltage
19.1
IrVc
IrEV
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
The potential across the source of EMF is equal to the sum of the potential drops across the resistors
19.2
nT IIII ....21
nT VVVV ....21
Resistors in Series and in Parallel
Since potential can be defined as
We can rewrite the equation for potential as
19.2
IRV
nT VVVV ....21 nneqT RIRIRIRI ....2211 neq RRRR ....21
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
The current through the source of EMF is equal to the sum of the current through the resistors
19.2
nT VVVV ....21
nT IIII ....21
Resistors in Series and in Parallel
Since current can be defined as
We can rewrite the equation for potential as
19.2
R
VI
nT IIII ....21 n
n
eq
T
R
V
R
V
R
V
R
V....
2
2
1
1 neq RRRR
1....
111
21
Resistors in Series and in Parallel
Circuits that contain both series and parallel components need to be solved in pieces
This circuit contains20 resistors in series25 resistors and load series to each
other and parallel to the 40 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
19.3
321 III
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
19.3
03255 31 VIIV
Kirchoff’s Rules
Steps
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
19.3
I1 I2I3
0321 III
Kirchoff’s Rules
Steps
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 positive if it goes in the direction of the loop
b. For a battery, the value is positive if the loop goes from – to + (nub to big end) 19.3
I1 I2I3
Kirchoff’s Rules
Steps
We’ll do the two inside loops
6. Combine the equations and solve
19.3
I1 I2I3
021343111 RIERIRIE
0232433 ERIRIE
DC Circuits
19.5 Circuits Containing Capacitors in Series and in Parallel
Circuits Containing Capacitors
19.5
For a parallel set of
capacitors – the total
charge is the sum of
the individual charges
In all parallel circuits – the potential across each branch is the same as the total
nT QQQQ ..21
nT VVVV ..21
Circuits Containing Capacitors
19.5
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
And
We combine and get
nT QQQQ ..21
CVQ
nnTeq VCVCVCVC ..2211 neq CCCC ..21
Circuits Containing Capacitors
19.5
Series capacitors
The magnitude of the charges is the same on each plate
nT QQQQ ..21
Circuits Containing Capacitors
19.5
The total potential is the sum of the potential drops across each capacitor
We then use that equation and the equation for capacitance
We get
nT VVVV ..21
C
QV
n
n
eq
T
C
Q
C
Q
C
Q
C
Q..
2
2
1
1 neq CCCC
1..
111
21
DC Circuits
19.6 RC Circuits-Resistors and Capacitors in Series
RC Circuits
19.5
Used
windshield wipers
timing of traffic lights
camera flashes