For a first-order process characterized by a resistance R and a capacitance C (electrical or analogous thermal/fluid storage), what is the time constant τ expressed in terms of R and C?

Introduction / Context:
First-order dynamics appear in RC circuits, well-mixed tanks with linear resistances, and thermal systems with lumped capacitance. The time constant τ determines how quickly the system output approaches its new steady state after a step input.

Given Data / Assumptions:

• Linear first-order model with a single energy/mass storage element.
• R denotes resistance to flow/heat/electric current.
• C denotes capacitance (storage capacity).

Concept / Approach:
In standard form, the first-order differential equation is τ dy/dt + y = K u, where τ is the time constant. For an RC circuit, τ = R * C in seconds. This generalizes via analogies: hydraulic (R = flow resistance, C = tank capacity), thermal (R = thermal resistance, C = heat capacity), etc. The product RC sets the exponential rise/decay speed: y(t) reaches about 63.2% of its final value in one τ.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis: [R]*[C] gives seconds in both electrical and analogous domains, confirming consistency.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing τ with 1/(RC); the exponential form must be carefully read to avoid inversion errors.

Final Answer:
RC