Transcript Electric Circuits

Chapter 20
Basic Electric Circuits
Units of Chapter 20
Resistances in Series, Parallel, and Series–
Parallel Combinations
Multiloop Circuits and Kirchhoff’s Rules
Ammeters and Voltmeters
Household Circuits and Electrical Safety
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
Resistors in series all have the same
current.
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
The sum of the voltages across each resistor
equals the battery voltage; after some algebra
this gives:
This formula is valid for any number of
resistors in series.
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
Resistors in parallel all have the same voltage.
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
The total current is the sum of the currents
through each resistor. After some algebra, we
find for the inverse of the equivalent
resistance:
In order to find the equivalent resistance,
you will need to invert your result.
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
The equivalent resistance of resistors in series
is always greater than any individual
resistance in the series.
The equivalent resistance of resistors in
parallel is always less than any individual
resistance in the array.
WHY??
20.6-20.7 Resistances in Series, Parallel,
and Series–Parallel Combinations
For combination circuits, simplify piece by piece.
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
Many circuits are not pure series–parallel
combinations; more sophisticated tools are
necessary to analyze them.
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
Kirchhoff’s first rule is the junction rule:
The sum of all current entering a junction
must equal the sum of all current leaving it.
Giving incoming current a positive sign and
outgoing a negative sign,
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
Kirchhoff’s second rule is
the loop rule:
The sum of the potential
differences around a
closed loop is zero.
Sign conventions for
traversing batteries and
resistors are at left.
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
1. Assign directional currents to
each branch of the circuit.
2. Identify enough loops so that
every branch is in a loop.
3. Apply the junction rule, keeping
independent equations.
4. Apply the loop rule. You should
have as many equations as
there are different currents.
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
1. Done!
2. Done!
3. Apply the junction rule, keeping
independent equations.
I1 - I2 - I3 = 0
OR
I1 = I2 + I3… eqn 1
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
1. Done!
2. Done!
3. Done!
4. Apply the loop rule. You should
have as many equations as
there are different currents.
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
4. Apply the loop rule. You should
have as many equations as there
are different currents.
Loop #1
ΣV = V1 + (-I1R1) + (-V2) + (I3R3) = 0
Eqn 2
*take 5… substitute & simplify
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
4. Apply the loop rule. You should
have as many equations as there
are different currents.
Loop #2
ΣV = V2 + (-I2R2) + (I3R3) = 0
Eqn 3
*take 5… substitute & simplify
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
4. Apply the loop rule. You should
have as many equations as there
are different currents.
Loop #3
No need… redundant equation!
Only the number of loops that
includes each branch once are
needed!
20.8-20.10 Multiloop Circuits and
Kirchhoff’s Rules
I1 = I2 + I3…
Eqn 1
ΣV = V1 + (-I1R1) + (-V2) + (I3R3) = 0
Eqn 2
ΣV = V2 + (-I2R2) + (I3R3) = 0
Eqn 3
Substitute and Solve!!!
20.11 Ammeters and Voltmeters
The deflection of a
galvanometer is
proportional to the
current.
20.11 Ammeters and Voltmeters
An ammeter measures current. In order to do
this, it must be connected in series; so as not
to change the existing current significantly, its
resistance should be as small as possible.
20.11 Ammeters and Voltmeters
A voltmeter measures
voltage. In order to do this,
it must be connected in
parallel across the voltage
to be measured; so as not
to change the existing
voltage significantly, its
resistance should be as
large as possible.
20.11 Ammeters and Voltmeters
Multirange meters have a selection of shunt
and multiplier resistors, to optimize the
measurement of currents and voltages of
different magnitudes.
20.14 Household Circuits and
Electrical Safety
Household wiring
is done in parallel
and protected by
circuit breakers.
20.14 Household Circuits and
Electrical Safety
Fuses are designed so the
fuse strip melts and cuts
the circuit if the current
exceeds a predetermined
value. Fuses are rated for
different currents; the fuse
rating should always match
the maximum allowable
current in the circuit. When
a fuse burns out, it must be
replaced.
20.14 Household Circuits and
Electrical Safety
Circuit breakers are used in most newer homes.
A bimetallic strip opens the circuit if the current
becomes too high; if a circuit breaker trips, it
can be reset.
Review of Chapter 20
Equivalent resistance of resistors in series:
Inverse of the equivalent resistance of
resistors in parallel:
Review of Chapter 20
Junction theorem: Algebraic sum of currents
entering a junction is zero.
Loop theorem: Algebraic sum of voltage drops
around a loop is zero.
An ammeter measures current, and should
have small resistance.
A voltmeter measures voltage, and should
have a large resistance.