Interdisciplinary Electrical Analogies

Electrical circuit analogies for several engineering disciplines have been developed over time. These are summarized in the table below prepared by Dr. Holbert. The mechanical analogy used is the mobility analogy in which the physical analogies are sacrificed in favor of creating equivalent mathematical relationships which hold in network analysis.

INTERDISCIPLINARY ANALOGIES
General Electrical Mechanical
Translational / Rotational		 Hydraulic
(Acoustic)		 Thermal
Flow Variable
(through variable)		 Current, I = dq/dt [Amps] Force, F [Newtons] Torque, T [Newton meters] Volume (fluid) flow, G [m³/s] Heat flow, q [Joules/sec]
Potential Variable
(across variable)		 Voltage, V [Volts] Velocity, v [m/sec] Angular velocity, w [radians/sec] Pressure drop, p [Pascals] Temperature difference, T [°C]
Integrating Element
(Delay Component)		 Inductance, L [Henrys]
Faraday's Law:
I = INT V dt / L		 Elasticity
Hooke's Law:
F = k INT v dt
k = spring constant (stiffness)		 Elasticity (e.g., torsion bar or coil spring)
T = k INT w dt
k = torsional spring constant		 Inertance, M
G = INT p dt / M
e.g., for pipe:
M = rho L/A		 Not Applicable
Proportional Element
(Dissipative Component)		 Resistance,
R = rho L/A [Ohms]
Ohm's Law:
I = V/R		 Viscous friction (e.g., dashpot or damper)
F = B v
B = damping constant		 Viscous friction
T = D w
D = damping factor		 Fluid resistance, R
G = p / R		 Heat transfer resistance, R
q = T / R
Rconvect = 1/(h A)
Differentiating Element
(Accumulative Component)		 Capacitance,
C = e A/d [Farads]
I = C dV/dt		 Mass (i.e., inertia), m [kg]
Newton's Second Law of Motion
F = m dv/dt		 Polar Moment of Inertia, J
T = J dw/dt		 Fluid capacitance, C
G = C dp/dt		 Thermal heat capacity, m cp
q = m cp dT/dt
Other Variables Charge,
q = INT I dt [Coulombs]		 Displacement,
x = INT v dt		 Angle, ß = INT w dt Flow velocity,
u = G/A [m/s]
Volume,
V = INT G dt [m³]		 Heat,
Q = INT q dt [Joules]
Junction/Node Law
SUM (Flow) = 0		 Kirchhoff's Current Law
SUM I = 0		 d'Alembert's Principle
SUM F = 0		 Second Law of Rotational Mechanical Systems
SUM T = 0		 SUM G = 0 SUM q = 0
Closed Loop Law
SUM (Potential) = 0		 Kirchhoff's Voltage Law
SUM V = 0		 Continuity of Space Law
SUM v = 0		 SUM w = 0 SUM p = 0 SUM T = 0
Power = (Potential)(Flow) P = I V [Watts] P = F v P = T w P = G p P = T q [Watts °C]
Kinetic Energy Ek = ½ L I² [Joules] Ek = ½ m v² Ek = ½ J w² Ek = ½ M G² Not applicable
Potential Energy Ep = ½ q²/C [Joules] Ep = ½ k x² Ep = ½ k ß² Ep = ½ [INT G dt]² / C Not applicable

Bibliography

  1. R.S. Sanford, Physical Networks, 1965, p. 113.
  2. G.F. Paskusz, B. Bussell, Linear Circuit Analysis, 1963, pp. 10-20, 29-43.
  3. A.G.J. MacFarlane, Dynamical System Models, Harrap, London, 1970, pp. 301-4.
  4. E.O. Doebelin, System Dynamics: Modeling and Response, Merrill Publishing Co., Columbus, OH, 1972.
  5. H.E. Koenig, W.A. Blackwell, Electromechanical System Theory, 1961, pp. 36-41.
  6. H.E. Koenig et al., Analysis of Discrete Physical Systems, 1967, p. 41.
  7. H.R. Martens, D.R. Allen, Introduction to Systems Theory, Merrill Publishing Co., Columbus, OH, 1969, pp. 23, 36-37, 43-72.
  8. Harry F. Olson, Solutions of Engineering Problems by Dynamical Analogies, D. Van Nostrand, 1966, pp. 33-35. [Uses classical analogy.]

Last updated: December 8, 2003
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