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Asked in NEET 1992 · Charging transients and time constant
The charge on a capacitor charging through a resistor grows as
q=q₀(1-e^-t/CR).
Whatever sits in the exponent beside t must itself be a time, so the time constant is
τ=CR.
Dimensionally, C is coulomb per volt and R is volt per ampere, so CR is coulomb per ampere,
which is a second.
After one time constant the capacitor has reached 1-e⁻¹≈63% of its final charge.
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