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.

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]Faraday's Law: I = V dt / L |
Elasticity Hooke's Law: F = k v dtk = spring constant (stiffness) |
Elasticity (e.g., torsion bar or coil spring)T = k dtk = torsional spring constant |
Inertance, MG = p dt / Me.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 vB = damping constant |
Viscous frictionT = D wD = damping factor |
Fluid resistance, RG = p / R |
Heat transfer resistance, Rq = T / RR _{convect} = 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, JT = J d/dt |
Fluid capacitance, CG = C dp/dt |
Thermal heat capacity, m c_{p}q = m c_{p} 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 LawI = 0 |
d'Alembert's PrincipleF = 0 |
Second Law of Rotational Mechanical SystemsT = 0 |
G = 0 |
q = 0 |

Closed Loop Law (Potential) = 0 |
Kirchhoff's Voltage LawV = 0 |
Continuity of Space Lawv = 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 | E_{k} = ½ L I² [Joules] |
E_{k} = ½ m v² |
E_{k} = ½ J ² |
E_{k} = ½ M G² |
Not applicable |

Potential Energy | E_{p} = ½ q²/C [Joules] |
E_{p} = ½ k x² |
E_{p} = ½ k ß² |
E_{p} = ½ [ G dt]² / C |
Not applicable |

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

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