You can label all known and unknown resistances, emfs, and currents with a clear circuit diagram.
You have to assign a direction if the current is unknown.
This is needed to determine the signs of potential changes.
The current will have a negative value if you assign the direction wrong.
The junction rule can be applied to any junction in the circuit.
If you don't get an equation with a current that doesn't show up in a previous application, then the equation is redundant.
The loop rule can be applied to as many loops as needed to solve the problem.
The loop rule requires you to choose a direction.
There are simultaneous equations for unknowns.
Carefully checking and rechecking may be required in this case.
Check to see if the answers are reasonable.
The numbers should be of the correct order of magnitude.
No resistance should be negative for the signs.
Check to see if the values obtained satisfy the various equations obtained from applying the rules.
The currents should satisfy the junction rule.
In theory, the material in this section is correct.
We should be able to verify it by measuring the current and voltage.
Some of the devices used to make such measurements are straightforward applications of the principles covered so far and are explored in the next modules.
Making a measurement changes the quantity being measured.
The rules can be applied to any circuit since they are for circuits of two laws.
The most broadly applicable principles in physics are conserve laws.
The rules for series and parallel in simpler circuits are usually simpler to use than the rules for more complicated situations.
The rules for series and parallel can be derived.
One of the basic analysis devices in circuit analysis can be expanded to include devices other than resistors and emfs.
Digital cameras, cell phones, and tuning-amplifiers are some of the meters in automobile dashboards.
The internal construction of the simplest of these meters and how they are connected to the system they monitor give further insight into applications of series and parallel connections.
The fuel and temperature gauge in this 1996 Volkswagen show the amount of gasoline in the tank and the engine temperature.
Whatever device's voltage is to be measured is connected to a voltmeter.
The objects in parallel experience the same potential difference.
Ammeters connect in series with the device's current to be measured.
The objects in a series have the same current.
The terminal voltage is measured between points a and b.
It's not possible to connect thevoltmeter directly across the emf without including its internal resistance.
An ammeter is used to measure current.
The current flows through the meter.
If the ammeter is located between points d and e it will have the same reading.
Current flow through a galvanometer causes a proportional needle deflection.
The resistance and current sensitivity of a galvanometer are crucial.
A galvanometer with a current sensitivity that has a maximum deflection of its needle can read half-scale when it flows through it.
If the galvanometer has a resistance, a full scale reading can only be produced by a single voltage.
You can use the galvanometer to measure a broad range of voltages or currents by connecting the resistors to it.
Figure 21.29 shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance.
The value of the resistance is determined by the maximum.
If you want 10 V to produce a full-scale deflection of a voltmeter with a galvanometer, suppose you want it to have a sensitivity.
10 V applied to the meter must produce a current.
The voltmeter's reading is proportional to the number of V applied to it, because 5 V produces a halfscale deflection by producing a current through the meter.
The meter would be difficult to read accurately, and it wouldn't be useful for voltages less than half a watt.
Other resistances are placed in series with the galvanometer.
Many meters have scales.
The galvanometer can be used to switch an appropriate resistance into a series.
A galvanometer G can be used to produce a voltmeter, the full-scale deflection of which depends on the choice of the resistance.
The larger the measure, the bigger it must be.
Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those produced by the galvanometer.
A galvanometer with the same sensitivity is needed for an ammeter that will give a full-scale deflection for 1.0 A.
The voltage across them is the same.
The ammeter depends on the choice of the galvanometer and the small resistance placed in parallel with it.
The galvanometer is protected from most of the current flowing through the meter.
Multiple scales may allow for greater flexibility in application.
The larger the current to be measured, the smaller the shunt resistance must be.
When you use an ammeter, you connect another Resistor to an existing circuit in order to change the circuit.
It is important to examine the circumstances under which the ammeter and the voltmeter do or do not affect the circuit.
The voltmeter is always placed in close proximity to the device being measured.
If the resistance is a few orders of magnitude greater than the device, the circuit won't be affected.
The two in parallel have a smaller resistance than the device being measured.
When the voltmeter is out of the circuit, the voltage across the device is not the same as it is when it is in.
This is an example of a significant change to the circuit.
An ammeter is placed in a series in the branch of the circuit being measured.
Normally, the ammeter's resistance is very small compared with the resistance of the devices in the circuit, and so the extra resistance is negligible.
If the ammeter is not as low in resistance as it should be, the total series resistance is significantly greater, and the current in the branch being measured is reduced.
There is a practical problem if the ammeter is not connected correctly.
If the ammeter was used to measure the current in the circuit, it would allow most of the current in the circuit to go through the galvanometer, and this current would be larger since the effective resistance is smaller.
The ammeter is not present in the circuit.
The circuit is to be avoided.
galvanometers with greater sensitivity are one solution to the problem of ammeters interfering with circuits being measured.
When less sensitive galvanometers are used, this allows the construction of voltmeters with greater resistance and ammeters with smaller resistance.
There are limits to galvanometer sensitivity, but it is possible to get meters that are accurate to a few percent.
The inaccuracy comes from altering the circuit, not from a fault in the meter.
The system being measured in a way that produces uncertainty is altered by making a measurement.
Alteration can be made negligibly small, but it can't be eliminated completely.
Measurement alters the system in a way that cannot be made small.
This limits nature's knowledge of the system.
The Heisenberg uncertainty principle will be discussed in the modules on quantum mechanics.
Drawing no current at all and not altering the circuit is a measurement technique.
null measurements are the topic of null measurements.
Digital meters that use solid-state electronics can give accuracies of one part.
Digital meters can detect smaller currents than analog meters.
Digital meters require less current than analog meters.
Their resistance as an ammeter can be less than that of an analog meter.
Stimulate a neuron and watch what happens.
In order to observe the ion as they move across the neuron membrane, Pause, rewind, and move forward in time.