Download ppt - plutonium

Chapter 26
DC Circuits
Units of Chapter 26
• 26.1 EMF and Terminal Voltage - 1, 2
• 26.2 Resistors in Series and in Parallel - 3,
4, 5, 6, 7
• 26.3 Kirchhoff’s Rules - 8, 9, 10
• 26.4 Circuits Containing Resistor and
Capacitor (RC Circuits) - 11, 12, 13
• 26.5 DC Ammeters and Voltmeters - 14, 15
• Electrical Hazards
26.1 EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current – these are called sources of
emf.
Battery is a nearly constant voltage source, but
does have a small internal resistance, which
reduces the actual voltage from the ideal emf:
26.1 EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
26.1 EMF and Terminal Voltage
Application #1:
A 65.0- resistor is connected
to the terminals of a battery
whose emf is 12.0 V and whose
internal resistance is 0.5 .
Calculate (a) the current in the
circuit, (b) the terminal voltage
of the battery, Vab, and (c) the
power dissipated in the
resistor R and in the battery’s
internal resistance r.
26.2 Resistors in Series and in Parallel
A series connection has a single path from
the battery, through each circuit element in
turn, then back to the battery.
26.2 Resistors in Series and in Parallel
The current through each resistor is the same;
the voltage depends on the resistance. The
sum of the voltage drops across the resistors
equals the battery voltage.
(26-2)
26.2 Resistors in Series and in Parallel
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit).
(26-2)
26.2 Resistors in Series and in Parallel
A parallel connection splits the current; the
voltage across each resistor is the same:
26.2 Resistors in Series and in Parallel
The total current is the sum of the currents
across each resistor:
26.2 Resistors in Series and in Parallel
This gives the reciprocal of the equivalent
resistance:
(26-3)
26.2 Resistors in Series and in Parallel
An analogy using
water may be helpful
in visualizing
parallel circuits:
26.2 Resistors in Series and in Parallel
Application #2:
(a) The lightbulbs in the example below are
identical and have identical resistance R.
What configuration produces more light?
(b) Which way do you think the headlights of a
car are wired?
26.2 Resistors in Series and in Parallel
Application #3:
Equivalent
Resistance
(a) What is the
equivalent
resistance in the
circuit to the right?
26.2 Resistors in Series and in Parallel
Application #4:
Two 100- resistors are
connected (a) in parallel, and
(b) in series to a 24.0-V
battery. What is the current
through each resistor and
what is the equivalent
resistance of each circuit?
26.2 Resistors in Series and in Parallel
Application #5:
(a) How much current flows from the battery in
the circuit? (b) What is the current flowing
through the 500- resistor in the circuit?
26.2 Resistors in Series and in Parallel
Application #6:
If a circuit has three identical lightbulbs of
resistance R, how does the brightness of
bulbs A and B compare with that of bulb C
when the switch is (a) open and (b) closed?
26.2 Resistors in Series and in Parallel
Application #7:
(a) Estimate the equivalent resistance of the “ladder”
of equal 250- resistors in the circuit. (b) What is
the current flowing through each of the three
resistors on the left if a 48.0 V battery is connected
between points A and B?
26.3 Kirchhoff’s Rules
Some circuits cannot be broken down into
series and parallel connections.
26.3 Kirchhoff’s Rules
For these circuits we use Kirchhoff’s rules.
Junction rule: The sum of currents entering a
junction equals the sum of the currents
leaving it.
26.3 Kirchhoff’s Rules
Loop rule: The sum of
the changes in
potential around a
closed loop is zero.
26.3 Kirchhoff’s Rules
Problem Solving: Kirchhoff’s Rules
1. Label each current.
2. Identify unknowns.
3. Apply junction and loop rules; you will
need as many independent equations as
there are unknowns.
4. Solve the equations, being careful with
signs.
26.3 Kirchhoff’s Rules
Application #8:
Calculate the currents I1, I2, and I3 in each of
the branches of the circuit.
26.2 Resistors in Series and in Parallel
Application #9:
(a) Determine the current in each part of the “ladder”
circuit of equal 250- resistors in the circuit if a 48.0
V battery is connected between points A and B. (b)
What would it be if the middle circuit has 200-
resistors and the right circuit has 300- resistors?
26.2 Resistors in Series and in Parallel
Application #10: The Marchand Box
(a) Determine the current in each part of the “ladder”
circuit of equal 100- resistors in the circuit if a 48.0
V battery is connected between points A and B?
Pinhead
26.3 Kirchhoff’s Rules
A Wheatstone bridge is a type
of “bridge circuit” used to
make measurements of
resistance. The unknown
resistance to be measured, Rx,
is placed in the circuit with
accurately known resistances
R1, R2, and R3. One of these,
R3, is a variable resistor which
is adjusted so that when the
switch is closed momentarily,
the ammeter shows zero
current flow.
26.3 Kirchhoff’s Rules
Application #11:
(a) Determine Rx in terms of R1, R2, and R3. (b) If a
Wheatstone bridge is “balanced” when R1 = 630 , R2
= 972 , and R3 = 42.6 , What is the value of the
unknown resistance?
26.3 Kirchhoff’s Rules
EMFs in series in the same direction: total
voltage is the sum of the separate voltages
26.3 Kirchhoff’s Rules
EMFs in series, opposite direction: total
voltage is the difference, but the lowervoltage battery is charged.
26.3 Kirchhoff’s Rules
EMFs in parallel only make sense if the
voltages are the same; this arrangement can
produce more current than a single emf.
26.3 Kirchhoff’s Rules
Application #12:
A good car battery is being used to
jump start a car with a weak
battery. The good battery has an
emf of 12.5 V and internal
resistance of 0.020 . Suppose
the weak battery has an emf of
10.1 V and internal resistance of
0.10 .
-continued on next slide-
26.3 Kirchhoff’s Rules
Application (con’t):
Each copper jumper cable is 3.0m
long and 0.50 cm in diameter, and
can be attached as shown. Assume
the starter motor can be represented
as a resistor Rs = 0.15 . Determine
the current through the starter motor
(a) if only the weak battery is
connected to it, (b) if the good
battery is also connected as shown.
26.3 Kirchhoff’s Rules
Application #13:
What would happen if the
jumper cables were mistakenly
connected in reverse, the
positive terminal of each battery
connected to the negative
terminal of the other battery?
Why could this be dangerous?
<Insert story here>
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
When the switch is closed, the capacitor will
begin to charge.
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
The voltage across the capacitor increases
with time:
(26-5b)
This is a type of exponential.
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
The charge follows a similar curve:

Q  CE 1  et RC

(26-5a)
This curve has a characteristic time constant:
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
The current I through the circuit at any time t
can be obtained by differentiating Eq. 26-5a:
dQ E t RC
I
 e
dt
R
(26-6)
Thus at t = 0, the current is
E
I
R
as expected for a circuit containing only a
resistor.
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
If an isolated charged capacitor is connected
across a resistor, it discharges:
(26-7)
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
The current I through the circuit at any time t
can be obtained by differentiating Eq. 26-5a:
dQ Q0 t RC
t RC
I

e
 I0e
dt RC
(26-8)
At t = 0, the current is equal to I0. The time it
takes to decrease to 37% of its original value is
t    RC
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
Application #14:
The capacitance in the circuit shown is C =
0.30 F, the total resistance is 20 k, and
the battery emf is 12 V. Determine (a) the
time constant, (b) the maximum charge the
capacitor could acquire, (c) the time it takes
for the charge to reach 99 % of the is value,
(d) the current I when the charge Q is half its
maximum value, (e) the maximum current,
and (f) the charge Q when the current I is
0.20 its maximum value.
26.4 Circuits Containing Resistor and
Capacitor (RC Circuits)
Application #15:
In the RC circuit shown, the battery has
fully charged the capacitor so Q0 = CE.
Then at t = 0 the switch is thrown from
position a to b. The battery emf is 20.0 V,
and the capacitance C = 1.02 F, the
current I is observed to decrease to 0.50
of its initial value in 40 s. (a) What is the
value of R? (b) What is the value of Q, the
charge on the capacitor at t = 0? (c) What
is Q at t = 60 s?
26.5 DC Ammeters and Voltmeters
An ammeter measures current; a voltmeter
measures voltage. Both are based on
galvanometers, unless they are digital.
The current in a circuit passes through the
ammeter; the ammeter should have low
resistance so as not to affect the current.
26.5 DC Ammeters and Voltmeters
A voltmeter should not affect the voltage across
the circuit element it is measuring; therefore its
resistance should be very large.
26.5 DC Ammeters and Voltmeters
An ohmmeter measures
resistance; it requires a
battery to provide a
current
26.5 DC Ammeters and Voltmeters
If the meter has too
much or (in this case)
too little resistance, it
can affect the
measurement.
26.5 DC Ammeters and Voltmeters
Application #16:
(a) Design an ammeter to read 1.0 A full scale
using a galvanometer with a full-scale
sensitivity of 50 A and a resistance of r = 30.
Check if the scale is linear.
(b) Using the same galvanometer with internal
resistance r = 30 and full-scale current
sensitivity of 50 A, design a voltmeter that
reads from 0 to 15 V. Is the scale linear?
26.5 DC Ammeters and Voltmeters
Application #17:
Suppose you are testing an electronic
circuit which has two resistors, R1 and
R2, each 15k, connected in series as
shown. The battery maintains 8.0 V
across them and has negligible
internal resistance. A voltmeter whose
sensitivity is 10,000 /V is put on the
5.0-V scale. What voltage does the
meter read when connected across R1,
and what error is caused by the finite
resistance of the meter?
Electric Hazards
Even very small currents – 10 to 100 mA can
be dangerous, disrupting the nervous system.
Larger currents may also cause burns.
Household voltage can be lethal if you are wet
and in good contact with the ground. Be
careful!
Electric Hazards
A person receiving a
shock has become part
of a complete circuit.
Electric Hazards
Faulty wiring and improper grounding can be
hazardous. Make sure electrical work is done by
a professional.
Electric Hazards
The safest plugs are those with three prongs;
they have a separate ground line.
Here is an example of household wiring – colors
can vary, though! Be sure you know which is the
hot wire before you do anything.
26.3 Kirchhoff’s Rules
Warm-Up:
Using the circuit to the right, draw a
picture showing how you would
connect (a) an ammeter to determine
the 3 currents, and (b) a voltmeter to
determine the potential drop across
each of the 5 resistances.
Summary of Chapter 26
• A source of emf transforms energy from
some other form to electrical energy
• A battery is a source of emf in parallel with an
internal resistance
• Resistors in series:
Summary of Chapter 26
• Resistors in parallel:
• Kirchhoff’s rules:
1. sum of currents entering a junction
equals sum of currents leaving it
2. total potential difference around closed
loop is zero
Summary of Chapter 26
• RC circuit has a characteristic time constant:
• To avoid shocks, don’t allow your body to
become part of a complete circuit
• Ammeter: measures current
• Voltmeter: measures voltage