Chapter 18
Basic Electric Circuits
Resistors in Series
18.1 Resistances in Series, Parallel,
and Series–Parallel Combinations
Resistors in series all have the same
current.
18.1 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.
Resistors in Parallel
18.1 Resistances in Series, Parallel,
and Series–Parallel Combinations
Resistors in parallel all have the same voltage.
18.1 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.
18.1 Resistances in Series, Parallel,
and Series–Parallel Combinations
Two handy things to remember:
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.
18.1 Resistances in Series, Parallel,
and Series–Parallel Combinations
For combination circuits, simplify piece by piece.
9V
15.0 Ω
10.0 Ω
6.0 Ω
9V
12.0 Ω
Find the current through the 5V battery
“BEEN THERE DONE THAT,
COME ON MR. MURPHY
HOW ABOUT A CHALLENGE
FOR ONCE?!?”
18.2 Multiloop Circuits and
Kirchhoff’s Rules
Many circuits are not pure series–parallel
combinations; more sophisticated tools are
necessary to analyze them.
18.2 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,
18.2 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.
18.2 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.
18.3 RC Circuits
An RC circuit can be used to
charge a capacitor through a
resistor.
18.3 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.
18.3 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.
18.3 RC Circuits
A charged capacitor may be
discharged through a
resistor; in this case no
battery is needed.
18.4 Ammeters and Voltmeters
The deflection of a
galvanometer is
proportional to the
current.
18.4 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.
18.4 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.
18.4 Ammeters and Voltmeters
Multirange meters have a selection of shunt and
multiplier resistors, to optimize the measurement
of currents and voltages of different magnitudes.
18.5 Household Circuits and
Electrical Safety
Household wiring is
done in parallel and
protected by circuit
breakers.
18.5 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.
18.5 Household Circuits and
Electrical Safety
Circuit breakers are used in most new homes. A
bimetallic strip opens the circuit if the current
becomes too high; if a circuit breaker trips, it can be
reset.
18.5 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.
18.5 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 of Chapter 18
Equivalent resistance of resistors in series:
Inverse of the equivalent resistance of
resistors in parallel:
Review of Chapter 18
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.