Connecting a capacitor to an inductor creates an oscillator. Once
started, charge flows back and forth between
the two sides of the capacitor at a fixed frequency, even after peak charge, voltage, and current decrease due to energy loss.
A hydraulic capacitor is a cylinder divided by a flexible rubber sheet.
Here's an oblique view and a cross-section side view.
A hydraulic inductor is a water wheel connected through a rigid axle to a
heavy stone flywheel, with a housing that forces the water in a
clockwise direction when the water flows from left to right.
Here's a conceptual view and a cross-section side view.
The following diagram shows an inductor-capacitor (L-C) circuit,
capacitor and inductor connected end-to-end. You start by pumping water
into the left side of the capacitor, pressurizing the water. The
potential energy is stored in the stretched rubber sheet separating the
two sides of the capacitor.
You remove the pump and allow the
circuit to run freely. The rubber sheet forces the water through the inductor, causing the
inductor's flywheel to spin faster and faster. When the rubber sheet
reaches the neutral position, the pressure is zero but the flywheel momentum and current are at
As the flywheel continues to turn, it pressurizes the
water and forces it into the opposite side of the capacitor, stretching
the rubber sheet in the opposite direction. When the flywheel runs out
of energy and stops, the capacitor is fully pressurized in the opposite
The same process runs in reverse, returning the circuit to
the original starting position if there is no friction. With loss of
energy to friction, the rubber membrane comes back into a less-stretched
maximum position, but it still oscillates with the same period.
For the electronic inductor-capacitor (L-C) circuit, you start by charging the capacitor,
raising the charge to the same voltage as a battery. The potential
energy is stored in the electric field that holds the charge on the two
sides of the capacitor. You disconnect the battery, connect the
capacitor to the inductor, and allow the circuit to run freely.
The voltage of the capacitor forces the accumulated charge through the
inductor, causing the inductor's magnetic flux to build up. The flux is
like the momentum of the flywheel in the hydraulic circuit. When the
capacitor runs out of charge, the voltage is zero but the flux and current are at their maximum.
The magnetic flux forces the current to continue flowing
into the opposite side of the capacitor, raising the voltage and
building up the charge across the capacitor in the opposite direction.
When the magnetic flux runs out of energy and the current stops flowing,
the capacitor is fully charged in the opposite direction.
process runs in reverse, returning the circuit to the original starting
point if there is no loss to wire resistance. With loss of energy
resistance, the capacitor carries less charge at the maximum point, but
it still oscillates with the same
If you take a charged capacitor as the
starting point (time=0), the voltage across the two devices is the
cosine function and the current through the circuit is the sine
Period = 2π SQRT(Inductance x Capacitance)
Frequency = 1/(Period)
The frequency of the oscillator does not depend on the amount of
charge. Charging the capacitor to a higher voltage increases the
amplitude of the voltage and current but does not affect the frequency.
This is just like a guitar string, which vibrates at the same frequency
whether plucked gently or strongly, producing the same note in either
case. Only the volume is affected. Like a guitar string, the amplitude dies away due to friction/resistance.
An L-C oscillator can be used as a tuner in a Crystal Radio
Capacitor Hydraulic Analogy
Inductor Hydraulic Analogy
LC Oscillator in Crystal Radio
Back to Main Hydraulic Analogy Page
Water circuit analogy to electric circuit
from HyperPhysics by C. Rod Nave, Georgia State University
Excellent resource for physics students
Hydraulic analogy, Wikipedia
Brief Wikipedia article, good overview
Understanding Electricity with Hydraulics
Describes hydraulic models for diodes, transistors, and op amps
Circuit Analysis, Khan Academy
Math analysis of electric circuits, including LC oscillator