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]

Faraday's Law:

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

R 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, J

T = J d /dt Fluid capacitance, C

G = 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 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 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

Bibliography