voltage dividers

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Figure 1 shows a voltage divider that consists of two resistors in series, connected to a voltage source. When resistors are placed in series the same current will flow through each of them. Using Ohm’s law we can calculate the current that flows through these resistors:

I = V / R
  = 5 / R1 + R2
  = 5 / 200
  = 0.025A

Therefore the ammeter would register a value of 0.025A. Since the current flowing through the circuit will be the same at any point, placing the ammeter at any point in the circuit will register the same value!

a voltage divider consisting of two resistors in series
Figure 1. a voltage divider consisting of two resistors in series

By connecting two or more resistors in series we can divide up the supply voltage into smaller amounts, since each resistor will have a voltage drop across it that is dependent on its resistance. This is the concept of voltage dividers.

Because we know the supply voltage and the resistances, we can calculate the voltage drop across each resistor by using the formula:

Vout = R2 / (R1 + R2) x Vin

Substituting the formula with the values for the circuit in figure 1:

Vout = R2 / (R1 + R2) x Vin
     = 100 / (100 + 100) x 5
     = 100 / (200) x 5
     = 2.5V

Therefore between points A and B the voltage will be 2.5V and between points B and C will be 2.5V.

Regardless of what the resistances are, as long as they are the same, the voltage across each one will be one-half of the voltage source!

Take a look at figure 2, where we now have 4 resistors. Once again, as long as all of the resistances are the same, the voltage across each resistor will be one-quarter of the voltage source.

Once again, let’s calculate what the voltage drop across each resistor is:

Vout = R1 / (R1 + R2 + R3 + R4) x Vin
     = 100 / (100 + 100 + 100 + 100) x 5
     = 100 / (400) x 5
     = 1.25V

Therefore between points A and B the voltage will be 1.25V, between points B and C will be 1.25V and between points C and D will be 1.25V.

a voltage divider consisting of four resistors in series
Figure 2. a voltage divider consisting of four resistors in series

Hopefully, from these two examples, you can see how useful voltage dividers can be to divide up voltages where required.

In figure 1 we have a power supply connected to two resistors, which are in series. Since we know the supply voltage and the resistance of the resistors, we can calculate the voltage drop across each resistor. To calculate the voltage across each resistor we use this formula:

power rating

As well as the resistance, there is another important value when using resistors, their power rating! Although voltage dividers are very useful, an important consideration is the power that is dissipated in the resistor! Resistors have a power rating, which is the maximum power that can be passed through them.

resistor datasheet showing power rating
Figure 3. resistor datasheet showing power rating

If we take the example circuit in figure 1, we can calculate the power that each resistor will have by using the formula I2 x R:

P = I2 x R
  = 0.0252 x 100
  = 0.000625 x 100
  = 0.0625W

Resistors often have a power rating that is in the range of 0.125 – 5W. All of these power ratings would be adequate for this circuit. It is very important that you make sure that you use a resistor with a suitable power rating. If you did use a resistor with a power rating that is too low, it will get hotter, smoke and possibly burn. You could also damage the circuit that the resistor is connected to! You cannot use a power rating lower than required but you can use one higher! For example, if you needed a resistor with a power rating of 0.25W but only had one with 0.5W, that would be fine.

conclusion

Voltage dividers are a very useful method of splitting a voltage up into smaller values. They have numerous application, such as in voltmeters and ohmmeters.