In the simple circuits we've seen, we have 0V known as ground at the negative end of the batteries in our circuits, and a positive voltage at the positive end of our batteries. In some circuits, especially in amplifiers, a negative voltage may be needed in addition to the ground. Our battery voltage has a positive in relation to ground, but it doesn’t have a negative voltage – Or does it? If you were to call the positive terminal on the battery Ground, then the negative terminal would now measure a negative voltage – But we’re only half way there, we’ve lost out positive voltage by measuring it this way.
You can try this using your multimeter with a 1.5V battery, placing the red (positive) lead probe at the positive terminal of the battery and the red (negative) lead probe to the negative terminal of the battery, you'll see it reads -1.5V
If we were to connect two of these batteries together in series (we connect the positive terminal of the first battery to the negative terminal of the second battery), we would some new ways to meaure the voltage...
Measuring the ends of the batteries (black probe on battery negative, red probe on battery positive) we would get 3V, which is expected in a series circuit. However, if you were to place the black probe where the batteries join, with the red probe still on the positive, you would get 1.5V. Placing the red probe on the negative end of our batteries would give us -1/5V.
We can see that the connection between the batteries can be used as a ground (0V), with a positive and a negative voltage in relation to this. This is great, if you have lots of batteries, but when if you only have 1 battery, and want to create a positive, negative and ground? This is where a voltage divider can be made with resistors, and it's a very simple principal that is often overlooked in beginner electronics tutorials.
If we connect 2 resistors in series to our battery, we have a voltage divider, which works by splitting the voltage, giving a positive at the battery positive terminal, a ground between the resistors, and a negative at the battery negative terminal.
If the resistor values are all equal, the voltage drop is divided equally between the resistors.
Here's the circuit again, showing some values being measured...
If we use different values for the resistors, the voltage drops are proportional to the resistor value differences.
We need to remember that we may need a higher voltage supply to ensure that there is enough voltage for the circuit as it’s being divided up by the resistors. A 9V battery if split equally, with only provide +4.5V and -4.5V in respect to ground. This may not be quite enough is a circuit needed a 5V power supply.
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