The time constant of a capacitor circuit is given by:

$\overline{){\mathbf{T}}{\mathbf{=}}{\mathbf{R}}{\mathbf{C}}}$

The charge stored in a capacitor and time are related by:

$\overline{)\begin{array}{rcl}\mathbf{Q}& \mathbf{=}& {\mathbf{Q}}_{\mathbf{0}}{\mathbf{e}}^{\mathbf{(}\mathbf{-}\mathbf{t}\mathbf{/}\mathbf{T}\mathbf{)}}\\ \mathbf{t}& \mathbf{=}& \mathbf{-}\mathbf{T}\mathbf{}\mathbf{ln}\mathbf{}\mathbf{\left(}\frac{\mathbf{Q}}{{\mathbf{Q}}_{\mathbf{0}}}\mathbf{\right)}\end{array}}$

A 20 μF capacitor initially charged to 25 μC is discharged through a 1.5 kΩ resistor.

How long does it take to reduce the capacitor's charge to 10 μC?

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