An uncharged capacitor C = 50 muF is charged through a resistor R = 100 kohms by a 10 V DC supply. What is the time constant tau and the charge on the capacitor after one time constant?

Answer and explanation

Correct answer: C. tau = 5 s, Q = 316 muC

  1. Step 1: Time constant: tau = R C = (100 10^3 ohms) (50 10^-6 F) = 5.0 s.
  2. Step 2: Maximum charge: Q_{max} = C V = (50 10^-6) * 10 = 500 muC.
  3. Step 3: Charge at t = tau: Q(tau) = Q_{max} (1 - e^-1) = 500 (1 - 0.3679) = 500 * 0.6321 = 316.05 muC.
Answer
tau = 5 s, Q = 316 muC.
Why not the others: tau = 0.5 s miscalculates 100k * 50u; Q = 500 muC is the final asymptotic charge at t -> infinity; tau = 2 s uses R = 40 kohms.

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