# Introduction to Control Systems 16

16. Spring constant in force-voltage analogy is analogous to :

(a) Capacitance
(b) Reciprocal of capacitance
(c) Current
(d) Resistance

Answer : (b)

Explanation :

Analogous Quantities :

 Electrical Quantity Mechanical Analog I Mechanical Analog II (Force-Current) (Force-Voltage) Voltage, e Velocity, v Force, f Current, i Force, f Velocity, v Resistance, R Lubricity, 1/B (Inverse friction) Friction, B Capacitance, C Mass, M Compliance, 1/K (Inverse spring constant) Inductance, L Compliance, 1/K (Inverse spring constant) Mass, M Transformer, N1:N2 Lever, L1:L2 Lever, L1:L2

Force-Current Analogy :

1. Mass (M) is analogous to Capacitor (C).
2. Force is analogous to current I.
3. Displacement (x) is analogous to flux (ψ).
4. Coefficient of friction (B) is analogous to resistance 1/ R and
5. Spring constant K is analogous to inverse of the inductor (L).

Force-Voltage Analogy :

1. Mass (M) is analogous to inductance (L).
2. Force is analogous to voltage V.
3. Displacement (x) is analogous to charge (Q).
4. Coefficient of friction (B) is analogous to resistance R and
5. Spring constant is analogous to inverse of the capacitor (C).

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