Transcript WBL6_Lecture_Ch18

Unit 8: Part 2
Electric Circuits
Outline
Resistances in Series, Parallel, and Series–
Parallel Combinations
Multiloop Circuits and Kirchhoff’s Rules
RC Circuits
Ammeters and Voltmeters
Household Circuits and Electrical Safety
Resistances in Series, Parallel, and
Series–Parallel Combinations
Resistors in series all have the same
current.
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.
Resistances in Series, Parallel, and
Series–Parallel Combinations
Resistors in parallel all have the same voltage.
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.
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.
Resistances in Series, Parallel, and
Series–Parallel Combinations
For combination circuits, simplify piece by piece.
Multiloop Circuits and Kirchhoff’s
Rules
Many circuits are not pure series–parallel
combinations; more sophisticated tools are
necessary to analyze them.
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,
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.
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.
Capacitance
A pair of parallel plates will store electric
energy if charged oppositely; this arrangement
is called a capacitor.
Capacitance
The charge is related to the potential
difference; the ratio is called the capacitance.
SI unit of capacitance: the farad, F
Capacitance
For a parallel-plate capacitor,
The quantity inside the parentheses is
called the permittivity of free space, and is
represented by ε0.
Capacitance
The energy stored in a
capacitor is the energy
required to charge it:
Dielectrics
“Dielectric” is another word for insulator. A
dielectric inside a capacitor increases the
capacitor’s energy storage by an amount
characterized by the dielectric constant, κ.
Dielectrics
A dielectric in an electric field becomes
polarized; this allows it to sustain a larger
electric field for the same potential difference.
Dielectrics
The capacitance of a capacitor containing a
dielectric is increased:
Dielectrics
Inserting a
dielectric into a
capacitor while
either the voltage
or the charge is
held constant has
the same effect—
the ratio of charge
to voltage
increases.
Capacitors in Series and in Parallel
Capacitors in series all have the same charge;
the total potential difference is the sum of the
potentials across each capacitor.
Note that this gives
the inverse of the
capacitance.
Capacitors in Series and in Parallel
We can picture capacitors in parallel as
forming one capacitor with a larger area:
Capacitors in Series and in Parallel
Capacitors in parallel all have the same potential
difference; the total charge is the sum of the
charge on each.
RC Circuits
An RC circuit can be used to
charge a capacitor through a
resistor.
RC Circuits
When the switch in an RC
circuit is closed, the current
has its maximum value (all
the voltage is across the
resistor), and the voltage
across the capacitor is zero.
As charge builds up on the
capacitor, the current
decreases and the capacitor
voltage increases.
RC Circuits
Voltage as a function of time:
Current as a function of time:
The quantity RC has the dimensions of
time, and is called the time constant.
RC Circuits
A charged capacitor may be
discharged through a
resistor; in this case no
battery is needed.
Ammeters and Voltmeters
The deflection of a
galvanometer is
proportional to the
current.
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.
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.
Ammeters and Voltmeters
Multirange meters have a selection of shunt
and multiplier resistors, to optimize the
measurement of currents and voltages of
different magnitudes.
Household Circuits and Electrical
Safety
Household wiring
is done in parallel
and protected by
circuit breakers.
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.
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.
Household Circuits and Electrical
Safety
In order to provide needed protection, the fuse
or circuit breaker needs to be on the “hot” side
of the circuit.
Household Circuits and Electrical
Safety
However, even on the hot side the fuse or breaker
may not protect the circuit. If an internal wire
touches the conductive casing of a tool or
appliance, you can still get a shock. This can be
avoided by using a
dedicated ground
line. You can tell
which devices
have such a line;
they have 3-prong
plugs.
Review
Equivalent resistance of resistors in series:
Inverse of the equivalent resistance of
resistors in parallel:
Review
Junction theorem: Algebraic sum of currents
entering a junction is zero.
Loop theorem: Algebraic sum of voltage drops
around a loop is zero.
Time constant for an RC circuit:
An ammeter measures current, and should
have small resistance.
A voltmeter measures voltage, and should
have a large resistance.