Introduction:
This resource includes the equations and rules that surround the topic of resistance and power, these are very important equations as you will need to know them to work with all but the most basic circuits.
All voltage is relative, so a reference point, called the 0 volt rail is used as a point of 0 volts relative to the rest of the circuit, the 0 volt rail is usually the wire connected to the negative terminal of the battery. Different types of ground are to be found in electronic circuitry, you will see the below ground very commonly in circuitry diagrams.
The symbol is that of an earth ground, a reference point with a voltage equal to that of earth. Technically, this symbol should not be used if there is no earth connection present, instead a signal ground should be used. Below are the images of different types of ground.
Signal ground is a point of 0 volts in the circuit, with no attachment to an earth rod. Chassis ground is a point of 0 volts in the circuit, with attachment to the metal chassis of a device. An earth grounding is used to disappate,
In a split voltage power supply, the arrangement so not so simple. A point of zero volts is still a lower potential than that of the positive supply, but higher potential than that of the negative supply.
1. Ohms law, resistance, voltage, and amperage
This is probably the most important equation in electronics. It states that:
I=V/R
the equation is also re-arrangeable to give
V=I*R
and
R=V/I
The reason this equation is so important is that it can be used to calculate current (measured in amps, however you will most likely encounter it in miliamps, which are thousandths of an amp), potential difference (measured in volts) and resistance (measured ohms) if the values of the other 2 are known it is possible to calculate the value.
Different people have differing analogies on resistance, current and potential difference. The hydraulic analogy is that the voltage between 2 points is the pressure difference (water flows from high pressure to low pressure areas, this was assumed to be the same with electric current, until it was discovered that electrons have negative charge and flow from areas of low potential difference to areas of high potential difference), the actual flow of the water is the current and a narrowing in the pipe acts like a resistor, making it harder for the water (electric current) to flow.
Voltage is measured between two points, across a component or section, whereas current is measured through a section. This is because the current is like water moving but potential difference is the pressure difference between the water (if you want to use the hydraulic analogy)
2. Power and energy
Watts are the unit of power. For electrical circuits power can be calculated by using this equation:
P=V*I
The potential difference between 2 points and the current flowing between these 2 points gives the power in watts. Power and energy are different things but there is an equation that links them:
E=t*P
This means that the power multiplied by the amount of time will give the energy output, like ohms law this equation can be re-arranged:
E/t=P
and
E/P=t
But because V=I*R the power equation can also be written
P=(I^2)R
The above equation applies only to purely resistive loads, useful for bug testing. Always keep this in mind.
The above equations you need to know for most circuits, ohm's law is used for calculating how much current is passing through an object, this can then be multiplied by the volts across the component to give the watts (like in the second equation). It is important to know the wattage a component is taking because components have maximum power ratings, exceeding this will cause the component to overheat and eventually (or rather quickly) destroy the component.
3. Resistance
There are two calculations needed for working out total resistance, one for resistors in series and one for resistors in parallel. It is important to know these as shops will not (usually, as *steve* pointed out) sell you a 258 ohm resistor or a 5 ohm resistor.
3.1 Resistors in series
The resistance calculation for resistors in series is very simple:
R1+R2+R3+R4... (carry on depending how many resistors are used) =Rtotal
3.2 Resistors in parallel
The resistance calculation for resistors in parallel is slightly less easy, and you should use a calculator:
1/(1/R1)+(1/R2)+(1/R3)+(1/R4)... (again carry on for how many resistors there are used) =Rtotal
Resistors can be used in combinations of parallel and series to give any resistor value you could want (or if you had unlimited, any value at all).
e.g. If I wanted a 258 resistor but I only had access to the standard preferred values
180+68+10= 258
e.g. If I wanted a 5 ohm resistor however I only have access to 10 ohm resistors
1/(1/10)+(1/10)= 5.
4. Series and parallel circuits
There are 2 ways of connecting multiple components together: in series and in parallel
4.1 Series circuits
In series circuits voltage is divided between the components (though usually not equally, the voltage across a component is proportional to the resistance of the component compared to the overall resistance of the series circuit) and the current is the same throughout the series circuit.
4.2 Parallel circuits
In parallel circuits the voltage is the same as the supply voltage across each branch and the current through each branch is divided up between the branches (though not usually equally)
4.3 Combinations
Series and parallel circuits can be used in combination. To work out current and potential differences at different points within these circuits you must think logically, combining the above rules for each section.
This resource includes the equations and rules that surround the topic of resistance and power, these are very important equations as you will need to know them to work with all but the most basic circuits.
All voltage is relative, so a reference point, called the 0 volt rail is used as a point of 0 volts relative to the rest of the circuit, the 0 volt rail is usually the wire connected to the negative terminal of the battery. Different types of ground are to be found in electronic circuitry, you will see the below ground very commonly in circuitry diagrams.
The symbol is that of an earth ground, a reference point with a voltage equal to that of earth. Technically, this symbol should not be used if there is no earth connection present, instead a signal ground should be used. Below are the images of different types of ground.
Signal ground is a point of 0 volts in the circuit, with no attachment to an earth rod. Chassis ground is a point of 0 volts in the circuit, with attachment to the metal chassis of a device. An earth grounding is used to disappate,
In a split voltage power supply, the arrangement so not so simple. A point of zero volts is still a lower potential than that of the positive supply, but higher potential than that of the negative supply.
1. Ohms law, resistance, voltage, and amperage
This is probably the most important equation in electronics. It states that:
I=V/R
the equation is also re-arrangeable to give
V=I*R
and
R=V/I
The reason this equation is so important is that it can be used to calculate current (measured in amps, however you will most likely encounter it in miliamps, which are thousandths of an amp), potential difference (measured in volts) and resistance (measured ohms) if the values of the other 2 are known it is possible to calculate the value.
Different people have differing analogies on resistance, current and potential difference. The hydraulic analogy is that the voltage between 2 points is the pressure difference (water flows from high pressure to low pressure areas, this was assumed to be the same with electric current, until it was discovered that electrons have negative charge and flow from areas of low potential difference to areas of high potential difference), the actual flow of the water is the current and a narrowing in the pipe acts like a resistor, making it harder for the water (electric current) to flow.
Voltage is measured between two points, across a component or section, whereas current is measured through a section. This is because the current is like water moving but potential difference is the pressure difference between the water (if you want to use the hydraulic analogy)
2. Power and energy
Watts are the unit of power. For electrical circuits power can be calculated by using this equation:
P=V*I
The potential difference between 2 points and the current flowing between these 2 points gives the power in watts. Power and energy are different things but there is an equation that links them:
E=t*P
This means that the power multiplied by the amount of time will give the energy output, like ohms law this equation can be re-arranged:
E/t=P
and
E/P=t
But because V=I*R the power equation can also be written
P=(I^2)R
The above equation applies only to purely resistive loads, useful for bug testing. Always keep this in mind.
The above equations you need to know for most circuits, ohm's law is used for calculating how much current is passing through an object, this can then be multiplied by the volts across the component to give the watts (like in the second equation). It is important to know the wattage a component is taking because components have maximum power ratings, exceeding this will cause the component to overheat and eventually (or rather quickly) destroy the component.
3. Resistance
There are two calculations needed for working out total resistance, one for resistors in series and one for resistors in parallel. It is important to know these as shops will not (usually, as *steve* pointed out) sell you a 258 ohm resistor or a 5 ohm resistor.
3.1 Resistors in series
The resistance calculation for resistors in series is very simple:
R1+R2+R3+R4... (carry on depending how many resistors are used) =Rtotal
3.2 Resistors in parallel
The resistance calculation for resistors in parallel is slightly less easy, and you should use a calculator:
1/(1/R1)+(1/R2)+(1/R3)+(1/R4)... (again carry on for how many resistors there are used) =Rtotal
Resistors can be used in combinations of parallel and series to give any resistor value you could want (or if you had unlimited, any value at all).
e.g. If I wanted a 258 resistor but I only had access to the standard preferred values
180+68+10= 258
e.g. If I wanted a 5 ohm resistor however I only have access to 10 ohm resistors
1/(1/10)+(1/10)= 5.
4. Series and parallel circuits
There are 2 ways of connecting multiple components together: in series and in parallel
4.1 Series circuits
In series circuits voltage is divided between the components (though usually not equally, the voltage across a component is proportional to the resistance of the component compared to the overall resistance of the series circuit) and the current is the same throughout the series circuit.
4.2 Parallel circuits
In parallel circuits the voltage is the same as the supply voltage across each branch and the current through each branch is divided up between the branches (though not usually equally)
4.3 Combinations
Series and parallel circuits can be used in combination. To work out current and potential differences at different points within these circuits you must think logically, combining the above rules for each section.
