As you saw in the last lab, the voltage-current relationship for a
resistor is V =
I*R where V is voltage measured across the resistor (in
Volts), I is the current through the resistor (in Amperes, or
Amps), and R is resistance value of the resistor (in Ohms).
This relationship is called Ohm's Law after the German scientist
George Ohm who proved the relationship experimentally in 1827. Ohm's
law may be applied to combinations of resistors, but because Ohm's Law
uses the total resistance of the circuit, it is important to know how to
combine resistances to find the
equivalent resistance.
1. For resistors in series, the result is just a simple sum, i.e.,
"resistors in series add."
2. However, for resistors in
parallel, the reciprocal of the equivalent resistance equals the sum of
the reciprocals of the resistors.
Now that is a mouth full!
3. This is better explained by the
following equations describing resistor combinations: (Req means
equilivent resistance.
It is the value for a single resistor which could be used in place
of all the other resistors.)
Series:
Parallel:
Another man, Kirchoff, came up with two other basic principles of circuits
Kirchoff's Voltage Law says that the sum of the voltages in a closed loop must equal zero. So, for a circuit consisting of a voltage source and several resistors in series,
the sum of the voltages across the resistors should be equal to the input voltage:
Vs = V1 + V2 +...Vn
where V1 + V2 + ... + Vn are the voltages across the resistors and Vs is the source voltage.
Kirchoff's Current Law states that the current flowing into a node must equal the current flowing out of a node. Therefore, in a parallel circuit, the current is split up at the node where the parallel branch starts and combined when the branch comes back together. In a series circuit, the same amount of current flows throughout:
Iin = Iout
Water Models
The relationships between voltage, current, and resistance can be related to water models representing circuits. The water pressure corresponds to voltage, the current is the flow rate, and the resistance is shown by constrictions in the pipes.
Basic Relationships:
Current in a Parallel Circuit:
Types of Circuits
Many things work because a circuit is complete. For example, the light in your car door only works (if it ever works) when the circuit is a closed loop. When you open the door, a plunger in the door frame retracts pulling the contacts of the circuit together, closing the loop. The light comes on. When the door is closed, the plunger pushes the contacts apart and the circuit is left open. Current can't flow and the light won't operate. Of course if you don't close the door completely then you get a dead battery because the circuit to the light stays closed.
The way a flashlight works is similar. When the flashlight is turned on, the switch closes the loop (the circuit) and the light comes on.
You can also short a circuit by placing a wire across one or more elements (resistors). Given the choice between a resistor and a wire, all the current flows through the wire (short circuit) because current follows the path of least resistance. The following pictures show the types of circuits we've discussed.
