Voltage dividers and electrical ground

[user111_23]

I'm confused about voltage divider circuits. I learned that the output voltage is larger than the input voltage when R1 is smaller than R2. Let's say R1=5Ohms and R2=10 and Vs=9V. Then Vo=6V! Why is the voltage lower? Did I do something wrong? (I used a voltage divider calculator, by the way.)

Also, how is electrical ground important in a DC circuit? Why do we use it for a reference point for voltage?

 

[vk6kro]

No, the output voltage is always smaller than the input voltage for simple dividers.

If you have two resistors in series and you put the input across both of them, the voltage across the individual resistors will add up to the the input voltage but will divide according to their resistances.

eg put 100 volts across a 30 ohm and a 20 ohm resistor in series.
the total resistance is 50 ohms (30 + 20), so the current will be 2 amps. (100 volts divided by 50 ohms is 2 amps)

So the voltage across the 30 ohm resistor will be 60 volts (2 amps times 30 ohms is 60 volts)
So the voltage across the 20 ohm resistor will be 40 volts (2 amps times 20 ohms is 40 volts)

Notice:
the voltages out are in the ratio of the resistor resistances.
the voltages add up to 100 volts which was the input voltage.
either of the voltages across the resistors is less than the input voltage.

Electrical ground is a useful concept. It means that you can safely join electrical grounds on different equipment together. You do this when you connect shielded cables between pieces of equipment.

Perhaps more importantly, it means that it is a safe place for humans to touch. Electrical ground is usually kept close to actual ground voltage so that you will not get a shock if you touched a metal part of the equipment and the kitchen sink at the same time, for example.