Download DC Circuits

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
S-123
A 35 cm long wire is hooked to a 1.5 V source.
It has a radius of 0.2 mm.
If a current of 6 A is measured in the wire,
what is its resistance?
What is the resistivity of the wire?
Birds in Series
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
S-124
Four resistors of 10 W, 20 W, 5 W, and 8 W
respectively are placed in series to a 12
volt source of EMF.
A. What is the total resistance of the circuit?
B. What is the total current?
C. What is the current
through each resistor?
D. What is the potential
drop across each
resistor?
World Series Champions
Now Married in some
Small 3rd World Countries
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 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
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
S-126
3 10W resistors are placed in a circuit
with a 6 volt source of EMF.
A.What is the equivalent resistance,
potential drop and current if they are
in series?
B.What if they are in parallel?
C.What if two are placed parallel to
each other then in series
with the third?
S-127
What is the the value for each current in the
circuit below?
I
I
R1 = 1 W
R2 = 2 W
I
R3 = 2 W
R4 = 1 W
E1 = 4 V
E2 = 2 V
1
3
2
S-129
What is the the value for each current in the
circuit below?
R1 = 1 W
R2 = 2 W
R3 = 2 W
R4 = 1 W
E1 = 4 V
E2 = 2 V
DC Circuits
19.6 RC Circuits-Resistors and Capacitors in
Series
RC Circuits
Used
windshield wipers
timing of traffic lights
camera flashes
When the switch is closed
current flows and
potential difference
across the capacitor
increases
19.6
RC Circuits
Eventually the potential difference across the
capacitor is equal to the EMF of the battery
Current is now zero
19.6
RC Circuits
The shape of the curve is given by

Vc  e 1  e
t
RC

RC = the time constant
Measures how quickly the capacitor becomes
charged
All circuits have some resistance, so they all
take time to charge
19.6
S-130
A 12 mF capacitor is placed in an RC circuit
with a single 10 W resistor. If the two are
placed in series with a 9 V source of EMF
and allowed to fully charge
A. What is the charge on the capacitor?
B. What is the current in the
resistor
C. How much energy is stored
in the capacitor?
S-127
Three 12 mF capacitor are placed in a circuit
across a 6 volt source of EMF.
A. What is the charge and potential difference
across each capacitor if they are in series?
B. What is the charge and potential difference
across each capacitor if
they are in parallel?
S-128
Three 12 mF capacitor are placed in a circuit
across a 6 volt source of EMF with one in
series and the other two parallel to each
other.
A. What is the equivalent capacitance of the
circuit?
B. What is the charge and
potential drop across each
capacitor?
S-129
All the resistors are 4 W, and each cell is 3 V.
What is the current in the center branch?
How much power is dissipated by that
resistor?
S-130
What is the charge and potential drop across
each of the following capacitors if they are
connected to a 12 V source of EMF??
C1 = 2 mF
C2 = 4 mF
C3 = 3 mF
C4 = 1 mF
C5 = 6 mF
C6 = 3 mF
Blank
S-131
Use Kirchoff’s laws to solve the following
problem. Calculate the current through
and potential across each resistor. Also
calculate the power dissipated in each
resistor.
V=3V
R1=5 W
R2=10 W
R3=5 W
R4=5 W
R5=10 W
Blank
S-132
Happy Test Day