# A 10 μF capacitor initially charged to 25 μC is

A 10 μF capacitor initially charged to 25 μC is discharged through a 1.4 kΩ resistor.
How long does it take to reduce the capacitor's charge to 10 μC?
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veiga34

Given:
Initial charge on the capacitor, ${Q}_{ο}=25µC$
Final charge on the capacitor, $Q=10µC$
Resistance, $R=1400\Omega$
Capacitance, $C=10\mu F$
Due to discharging, charge on the capacitor is calculated by
$Q={Q}_{0}{e}^{-t/RC}$
plug in the values
$10=25{e}^{t/1400×10×{10}^{-6}}$
$\frac{2}{5}{e}^{-t/14×{10}^{-3}}$
taking log both sides
$\mathrm{ln}\left(\frac{2}{5}\right)=\frac{-t}{14×{10}^{-3}}$
$=-0.916=-t×71.43$
$t=0.013s$