The number of time constants after which a circuit is considered at steady state.

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Multiple Choice

The number of time constants after which a circuit is considered at steady state.

Explanation:
The main idea is that the transient part of a first-order circuit (like RC or RL) decays exponentially with a time constant τ. After a few τ, the response is essentially at its final steady value. The remaining transient after n time constants is proportional to e^{-n}. At five time constants, the transient term is e^{-5} ≈ 0.0067, meaning about 0.67% of the initial transient remains and the circuit is within about 99.33% of its final value. Hence, five time constants is the standard rule of thumb for practical steady state. (Some contexts use 4τ or 3τ for looser criteria, but five τ is the common default.)

The main idea is that the transient part of a first-order circuit (like RC or RL) decays exponentially with a time constant τ. After a few τ, the response is essentially at its final steady value. The remaining transient after n time constants is proportional to e^{-n}. At five time constants, the transient term is e^{-5} ≈ 0.0067, meaning about 0.67% of the initial transient remains and the circuit is within about 99.33% of its final value. Hence, five time constants is the standard rule of thumb for practical steady state. (Some contexts use 4τ or 3τ for looser criteria, but five τ is the common default.)

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