A capacitor is charged and then made to discharge through a resistance

1.	A capacitor is charged and then made to discharge through a resistance. The time constant is τ. In what time will the potential difference across the capacitor decrease by 10%? (a) τ In (0.1) (b) τ In (0.9) (c) τ In (10/9) (d) τ In (11/10)
Answer» Correct Answer is:(c) τ In (10/9) Q = Q₀e ^-t/τ and potential difference across C is proportional to Q. For the p.d. to fall by 10%, Q must fall by 10%. Q = 0.9Q₀ = Q₀e ^-t/τ or e^t/τ = 10/9 or t/τ = In (10/9).

A capacitor is charged and then made to discharge through a resistance. The time constant is τ. In what time will the potential difference across the capacitor decrease by 10%? (a) τ In (0.1) (b) τ In (0.9) (c) τ In (10/9) (d) τ In (11/10)

Answer»

Correct Answer is:(c) τ In (10/9)

Q = Q₀e ^-t/τ and potential difference across C is proportional to Q. For the p.d. to fall by 10%, Q must fall by 10%.

Q = 0.9Q₀ = Q₀e ^-t/τ

or e^t/τ = 10/9

or t/τ = In (10/9).