Circuit and electromagnetism basics
A capacitor charged to 10 V is discharged through a resistor. Which is closest to the capacitor voltage after a time equal to the time constant τ?
- AAbout 3.7 V
- BAbout 6.3 V
- C5 V
Show answer and explanation
Answer: A. About 3.7 V
During discharge the voltage falls as v = V0 e^(−t/τ). At t = τ, e⁻¹ ≈ 0.368, so the voltage is 10 V × 0.368 ≈ 3.7 V. About 6.3 V is the value reached at t = τ during charging (1 − e⁻¹ ≈ 0.632); during discharge the answer is the starting voltage reduced by about 63%. After 2τ it is about 1.4 V, and after 5τ about 0.07 V, essentially fully discharged.
- A. Correct. 10 V × e⁻¹ ≈ 3.7 V.
- B. About 6.3 V is the charging value, confused with discharge.
- C. 5 V is half; at t = τ the voltage has already fallen below half, to about 3.7 V.
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