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Circuit and electromagnetism basics

What is the time constant of an RL circuit with a coil of inductance L = 10 mH in series with a resistor R = 100 Ω?

  1. A1 s
  2. B100 µs
  3. C1 ms
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Answer: B. 100 µs

The time constant of an RL circuit is τ = L/R: 10×10⁻³ H/100 Ω = 1×10⁻⁴ s = 100 µs. When a DC voltage is applied, the current reaches about 63% of its final value (E/R) after τ and is essentially final after 5τ = 500 µs. A larger resistance shortens the time constant—the opposite of an RC circuit (τ = RC), where a larger resistance lengthens it.

  • A. 1 s is L × R, not the time-constant formula τ = L/R.
  • B. Correct. 10 mH/100 Ω = 100 µs.
  • C. 1 ms is ten times too large, an order-of-magnitude error.
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