The dimensions of RC are

Asked in CBSE AIPMT 1995 · Dimensional formula of a named quantity

Answer: (3) time

Step-by-step solution

Idea: the charge on a capacitor decays as q=q₀e^-t/RC, so RC must be a time.

Check with units: R is in ohms and C is in farads.

ohm×farad=V/A×C/V=C/A=s

So RC has the dimensions of time, and it is called the time constant of the circuit.

(1) comes from confusing RC with LC, which is the square of a time
(2) comes from the reciprocal of that same slip
(4) comes from the reciprocal of the right answer; 1/(RC) is a frequency, and RC itself is the time constant

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