Electric circuits and the hydraulic analogy: force, energy, and power
Energy in the form of work is force times distance
Here we have a 1 kilogram mass resting on a table
in a uniform gravitational field
If I push up
against the field, I do work against this
mass, and if I allow the mas to press down against my hand it, does work
against my hand
Energy equals force times distance
The mass exerts a downward force of 9.8. Newtons
If the distance is 1 meter,
Then the energy in
moving the mass is 9.8 Newtons times 1 meter
Which is 9.8 joules
Now let's look at a similar situation in a hydraulic piston.
We have a uniform downward force on this piston due to the pressure of the water
If I push the piston up, I'm doing work against the water
If I allow the piston to press against my hand, it's doing work against my hand
Again, the energy is force times distance
What is the force? It's the pressure of the water multiplied by the area of the top of this piston
Now I can rearrange these parentheses like this: pressure
times area times distance, and what is the area
times distance? It is the volume of water displaced. You can see the area times this distance is the volume, so
energy equals pressure times volume
Standard units are Pascals and cubic meters, but Pascals are a very tiny unit of pressure, and a cubic meter is a very large
unit of volume, so we can make the first unit a thousand times bigger and
the second unit thousand times smaller. We get kPa and liters. If we have a displacement of two liters
and the pressure is 300 kPa, we have this much pressure this much volume, and that's 600 joules of energy
Now let's look at an electric example. We have a 100 volt battery and two parallel metal plates. We have a
negative voltage here and a positive voltage here
Here's the cross-section view of the same thing, 100 volt battery, positive on the bottom,
negative on the top. If there's a free electron between these two plates, you will feel a downward force because it's
attracted to the positive charge here and repelled by the negative charge here
Now suppose we have a piece of amber and we rub it with a fur. It will acquire a negative charge. Just like the electron
and will be attracted to this
positively charged plate and
it'll be repelled by this negatively charged plate
If I move this
piece of amber against the electric field, I'm doing work on it, and if I allow it to press down on my hand
it's doing work on my hand
How much is that work? Now, ignoring gravity and just considering the electric field, the energy is the
voltage times the charge. If this is 100 volt difference, and this is one Coulomb of charge,
then the energy is 100 volts times 1 Coulomb, equals 100 joules
So to summarize once again, energy
equals pressure times volume for a hydraulic system or
energy equals voltage times charge
for an electronic system.
In a hydraulic circuit, we have water in constant motion.
Starting with a reservoir of water at zero pressure,
this pump pressurizes the water to 300 kPa. There's not much
pressure drop in this wide pipe.
Tkihrough this narrow section, there's a drop in pressure from 300 to 0 lo kPa.
Let's say the flow is 0.1 liter per second.
The pump is
raising the energy levels, doing work at a certain rate, to raise the water to a higher pressure and
on this side, we recover the energy as heat as
the water drops in pressure from 300 to 0 kilo kPa
So we have
energy coming in here energy coming out here
as heat, and how much is that? Power equals energy per unit of time.
That's pressure times volume per unit of time.
That's the pressure times the flow rate.
We have 300 kPa pressure,
0.1 liter per second flow rate. That equals 30 watts.
So we have 30 watts of power coming into this pump to make it work and 30 watts of heat energy coming out of this
resistor.
The electric circuit is very similar: charge in constant motion.
We start with charge at zero volts. The battery draws up the charge and
pressurizes it, so to speak, to 1.5 volts.
It flows through this wire with
negligible voltage drop and then the voltage drops from 1.5 to zero as it goes through this resistor.
And let's say the current is 1 amp or 1 Coulomb per second.
The battery is
doing work on the charge, that is, raising it up from 0 to 1.5 volts.
And we recover that energy by allowing the voltage to drop from 1.5 volts to 0 volts.
So we have energy coming in here to
raise the voltage and energy coming out as heat
when the voltage drops to zero. we can do useful work by connecting a motor or
light bulb.
How much power is that?
In the hydraulic example it was power equals pressure times flow rate. For the electric circuit,
we have power equals voltage times current.
1.5 volts times 1 amp equals 1.5 watts.
So to summarize again
the
volume is like charge, flow rate is like current,
pressure is like voltage.
Energy is in joules, that is,
pressure times volume,
kPa-liters, or
voltage times charge, volt-coulombs
Power is
pressure
times flow rate,
kPa times liters per second, or in an electric circuit,
voltage times current, volts times amps