Electronics has certain basic components that can be found in almost all circuits. The Resistor, the Capacitor, and the inductor are the most common components found in most simple circuits. We will be focusing on the resistor and its equations in a series DC circuit.
The Resistor is generally made of carbon but may also be wire wound and is characterized by the ability to dissipate heat(or power) measured in watts. There are five sizes of carbon resistor.
1. 2 watt
2. 1 watt
3 1/2 watt
4. 1/4 watt
5. 1/8 watt
Any resistor that is rated for over 2 watts must be wire wound as opposed to carbon based. Rheostats have two connectors while Potentiometers have 3 connections.
Resistors may be fixed in value (ohms) or variable in value.
While it is possible for a short to occur around a resistor, Resistors will not short or at least not for long uncontrolled current running through a resistor that has shorted out will quickly cause the resistor to open breaking the circuit. You can see this effect by placing a 5 watt light bulb in a 200watt socket it may take some time but the bulb will eventually open or in layman's terms burn out.
A simple circuit can be created with a DC power source such as a battery and a load the resistance provided by a lamp can also be measured in Ohms and as such is equivalent to a wire wound resistor. The equation that is used is Ohms law I =E/R or Current is equal to Volts divided by ohms. so if we have a 1.5v battery attached to a 5ohm lamp the current is equal to .3 amps. Power is found with the following equation P(watts)=I(amps)*E(volts) so we know from the previous example that the power consumed is .45 watts because the .3 amps multiplied by the 1.5 volts is equal to the power.
The formula for a DC series circuit to find total resistance is
One must always keep in mind that Current is common(constant) in a DC series circuit. this means that no matter where you measure the current in a DC series circuit it will always be the same and is expressed by the following equation:
Kirchoff's law states that the Source Voltage must equal the voltage drop across all resistors in a DC series circuit and can be expressed as
The voltage drop equation is very useful for determining the the voltage drop across a single resistor which is spoken as the Voltage drop across resistor 1 is equal to the current at resistor 1 times the resistance of resistor 1 and can be expressed by the formula
So using our previous example we can say that .3amps*5ohms=1.5volts the exact voltage drop across our lamp which also turns out to agree with Kirchoff's law because it is equal to source voltage since we only have one resistor in the circuit.
While our example is quite simple by applying the principles to more complex circuits and using measuring equipment to get partial values for the entire circuit we can troubleshoot a circuit that is not operating properly and determine exactly what the problem is.