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.
I
1
- I
2
- I
3
= 0
OR
I
1
= I
2
+ I
3
… 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 = V
I
3
R
3
1
) = 0
+ (-I
1
R
1
) + (-V
2
) + (-
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 = V
2
+ (-I
2
R
2
) + (I
3
R
3
) = 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
I
1
= I
2
+ I
3
… Eqn 1
ΣV = V
I
3
R
3
1
) = 0
+ (-I
1
R
1
) + (-V
2
) + (-
Eqn 2
ΣV = V
2
+ (-I
2
R
2
) + (I
3
R
3
) = 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.