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Circuit and electromagnetism basics

What is the time constant of an RC circuit with a resistor R = 1 kΩ and a capacitor C = 10 µF in series?

  1. A10 ms
  2. B100 ms
  3. C1 ms
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Answer: A. 10 ms

The time constant of an RC circuit is τ = RC: 1×10³ Ω × 10×10⁻⁶ F = 1×10⁻² s = 10 ms. It is the time for the capacitor voltage to reach about 63% of its final value after a step input, and after 5τ (50 ms here) the voltage is essentially final (over 99%). Since ohms times farads gives seconds, the units provide a check on the calculation.

  • A. Correct. 1 kΩ × 10 µF = 10 ms.
  • B. 100 ms is ten times too large, an order-of-magnitude error.
  • C. 1 ms is ten times too small, an order-of-magnitude error.
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