Voltage Dividers

Today we talked about voltage dividers -

We used a DC Power supply and some resistors to measure what we built -

Here's the voltage divider example:

The circuit is as shown.  What is the value of V-out in volts?

The standard voltage divider equation is:

                                Vout = ((V-in)*R1)/(R1+R2)

So in this example we have:

     Vout = (20V*6.8MΩ

)/(6.8M

Ω

+6.8M

Ω

) = 10 volts

But we really don’t need to memorize a formula for this-

Good old Ohm’s Law will serve us just fine.

First, we need to find the total current flowing in the circuit...

To do that, we need to find the total resistance.

The total resistance here is just R1+R2

So the total current is found using Ohm’s Law - I = E/R

I = V-in*(R1 + R2) = 20V/13.6MΩ = 1.47 uA (micro-amps)

Now the voltage out is easy now that I know the current...

V out = I*(R1)

If we substitute the equation for I with this one, we get:

V out =  V-in*R1/(R1 + R2)

Which looks an awful lot like -

Vout = ((V-in)*R1)/(R1+R2)

Which is the standard voltage divider equation for two resistors.

We used a voltmeter to measure this.

The meter had 10 M

Ω input impedance.

We expected 10 volts like we calculated, right?

But we only read about 7.5 volts. (Actually, we read 7.45 volts)

Why?