A 10.0 μF capacitor initially charged to 20.0 μC is discharged through a 2.80 kΩ resistor. How long does it take to reduce the capacitor's charge to 10.0 μC?

19.4 ms

Step-by-step explanation:

The electric charge in a capacitor is given as;

Q = CV

Initial volts V = Q/C = 20µC/10µF = 2volts

final volts V = Q/C = 10µC/10µF = 1volts

Voltage on a capacitor undergoing discharge is given as;

v = v₀e^ (-t/τ)

Where;

v₀ = initial voltage on the capacitor

v = voltage after time t

R = resistance in ohms,

C = capacitance in farads

t = time in seconds

RC = τ = time constant

Therefore;

τ = 10µF x 2.8kΩ = 28 ms

v = v₀e^ (-t/τ)

1 = 2e^ (-t/28ms)

e^ (-t/28ms) = 0.5

-t/28ms = - 0.693

t = (28ms) (0.693) = 19.4 ms