# 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, [radians/sec] Pressure drop, p [Pascals] Temperature difference, T [°C]
Integrating Element
(Delay Component)
Inductance, L [Henrys]
I = V dt / L
Elasticity
Hooke's Law:
F = k v dt
k = spring constant (stiffness)
Elasticity (e.g., torsion bar or coil spring)
T = k  dt
k = torsional spring constant
Inertance, M
G = p dt / M
e.g., for pipe:
M = L/A
Not Applicable
Proportional Element
(Dissipative Component)
Resistance,
R = 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 = 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 d /dt
Fluid capacitance, C
G = C dp/dt
Thermal heat capacity, m cp
q = m cp dT/dt
Other Variables Charge,
q = I dt [Coulombs]
Displacement,
x = v dt
Angle, ß =  dt Flow velocity,
u = G/A [m/s]
Volume,
V = G dt [m³]
Heat,
Q = q dt [Joules]
Junction/Node Law (Flow) = 0
Kirchhoff's Current Law I = 0
d'Alembert's Principle F = 0
Second Law of Rotational Mechanical Systems T = 0 G = 0 q = 0
Closed Loop Law (Potential) = 0
Kirchhoff's Voltage Law V = 0
Continuity of Space Law v = 0  = 0 p = 0 T = 0
Power = (Potential)(Flow) P = I V [Watts] P = F v P = T P = G p P = T q [Watts °C]
Kinetic Energy Ek = ½ L I² [Joules] Ek = ½ m v² Ek = ½ J ² Ek = ½ M G² Not applicable
Potential Energy Ep = ½ q²/C [Joules] Ep = ½ k x² Ep = ½ k ß² Ep = ½ [ 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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