A 20.0 μF capacitor initially charged to 30.0 μC is discharged through a 1.20 kΩ resistor. How long does it take to reduce the capacitor's charge to 15.0 μC

16.6 ms or 0.0166 s

Explanation:

If Q is the final charge, Q' is the initial charge, C the capacitance, R is the resistance, t the time taken and τ the time constant,

[tex]Q = Q' (1 - e^{-t/div / tau })

τ = R C = (1.20*10³) (20*10⁻⁶) = 0.024 s

15 = 30 (1 - e^{-t/div / 0.024 })

(1 - e^{-t/div / 0.024 }) = 15 : 30

⇒ - e^{-t/div / 0.024 }) = 0.5 - 1

⇒ e^{-t/div / 0.024 }) = 0.5

Taking logarithm to the base e on both sides of this equation,

⇒ t = 0.0166 seconds = 16.6 milli seconds