Voltage Divider Rule (VDR) Explained

Voltage Divider Rule

Voltage divider rule or potential divider rule is a method used in electrical and electronics engineering to divide the input voltage into fractions by placing components in series. It is based on basic nature of electricity which divides voltage in series combination. 

In this simple circuit which is simulated or tested on Multisim , having two resistances R₁ and R₂  and a voltage source of 12 V, the voltage can be seen divided in voltmeters connected in parallel with them.

Total Voltage in circuit = 12 V

Voltage across R₁        = 4.286 V

Voltage across R₂        = 7.714 V

Sum of voltages           = 4.286 V + 7.714 V = 12 V

Which proves voltage divider rule experimentally.

One fact that you will notice quickly that the voltage drop across larger resistance is higher while that of lower resistance is lower which opposite of current divider rule.

Derivation Of Voltage Across Each Resistance Theoretically

To derive expression for voltages across each resistors theoretically in series combination, we will take a simple circuit as follows:

By applying ohm's law we know that:

v1= iR_{1  ---- (I)}

_v2 = iR_{2 ----(II)}

By applying VDR we have:

V = v1 + v2

Substituting the values of v1 and v2 we have:

V =  iR_{1 +} iR₂

_{V  =   i(}R_{1 +} R₂₎

_Or

i =  _V/ (R_{1 +} R_{2 )}

Now, to get the values of voltage across each resistor we substitute the value of i in equation I and II:

v_{1 =}  R_{1 x V /} (R_{1 +} R_{2 )}

_and

v_2 =  R_{2 x V /} (R_{1 +} R_{2 )}

For N number of resistors:

V_{n = Rn x v / (R1 + R2 + ...... + RN)}

_{We can also see theoretically as it was proved experimentally as above that the voltage is directly proportional to resistance across which voltage is determined which proves that the greater the resistance the greater would be the voltage across it.}

_{Now if compare it with CDR equation:}

We will realize that in CDR the resistance of adjacent next parallel resistance is required to multiply with total current as opposed to VDR in which the resistance across which voltage is to be measured is multiplied with total voltage. The rest is same for both CDR and VDR.

Applications Of VDR

1)Voltmeter

VDR is most commonly used to make glavanometer a voltmeter by connecting a resistor of high resistance as compared to glavanometer. As voltage drop across higher resistance is higher, this enables to pass a small fraction of voltage to galvanometer saving glavometer from burning.

Making of Voltmeter By Using VDR

2) Potentiometer

Another common application of VDR is in potentiometer. Potentiometer or "pot" is used to vary the voltage of signal. For example the knob used to vary sound  in our speakers or to vary  fan speed in fan dimmers is actually a pot. The most basic pot contain three pins. The first and last pin connected to variable resistor while the middle pin connected to a sliding contact which slides on the resistor when someone adjusts the knob thus changing the voltage according the resistance in variable resistor.

  

And to divide and vary voltage potentiometer must be connected  in series with voltage source as shown below:

In this simple buzzer circuit you can see that potentiometer is connected in with voltage source