A capacitor is discharged through a 100 ohm resistor. The discharge current decreases to 29% of its initial value in 2.8 ms. What is the value of the capacitor?
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voltage on a cap, discharging
v = v₀e^(–t/τ)
v₀ is the initial voltage on the cap
v is the voltage after time t
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
v/v₀ = e^(–t/τ) = 0.29
–t/τ = ln 0.29 = -1.238
τ = 2.8m / 1.238 = 0.00226
τ = RC = 100C = 0.00226
C = 0.0000226 = 22.6µF
v = v₀e^(–t/τ)
v₀ is the initial voltage on the cap
v is the voltage after time t
R is resistance in ohms,
C is capacitance in farads
t is time in seconds
RC = τ = time constant
v/v₀ = e^(–t/τ) = 0.29
–t/τ = ln 0.29 = -1.238
τ = 2.8m / 1.238 = 0.00226
τ = RC = 100C = 0.00226
C = 0.0000226 = 22.6µF