Question

The capacitance, in force-current analogy, is analogous to

• A. momentum
• B. velocity
• C. displacement
• D. mass

Hint:

Use this quick summary table for analogies:
- Force-Voltage (F-V): Mass ($M$) $\leftrightarrow$ Inductance ($L$).
- Force-Current (F-I): Mass ($M$) $\leftrightarrow$ Capacitance ($C$).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This question deals with analogous systems, specifically comparing translational mechanical systems with electrical systems using the Force-Current (F-I) analogy.

Step 2: Key Formula or Approach:
We compare the governing differential equations of a mechanical system and an electrical system:
- Mechanical (Newton's Second Law):
\[ F = M \frac{dv}{dt} \]
- Electrical (Capacitor Current):
\[ i = C \frac{dv_c}{dt} \]

Step 3: Detailed Explanation:
By comparing the equations:

• Force ($F$) is analogous to current ($i$).

• Velocity ($v$) is analogous to voltage ($v_c$).

• Therefore, mass ($M$) corresponds directly to capacitance ($C$).

• In this analogy (F-I), other terms are:
- Friction coefficient ($B$) is analogous to conductance ($1/R$).
- Spring constant ($K$) is analogous to the reciprocal of inductance ($1/L$).

Step 4: Final Answer:
In the force-current analogy, capacitance is analogous to mass, which corresponds to Option (D).