Question

If C and R denote capacitance and resistance. the dimensional formula of CR is

(a) [M⁰L⁰T¹]

(b) [M⁰L⁰T⁰]

(c) [M⁰L⁰T^-1]

(d) not expressible in terms of MLT.

Answer 1

Correct option (a) [M⁰L⁰T¹]

Explanation:

Capacitance C = charge/potential difference

Dimensions of c = [AT]/[ML²T^-3A^-1]  = [M^-1L^-2T⁴A²]

Resistance R = potential difference/Current

= [ML²T^-3A^-1]/[A] = [ML²T^-3A^-2]

Dimensional formula of CR

=  [M^-1L^-2T⁴A²] [ML²T^-3A^-2] = [T]

As the (CR) has dimensions of time and so is called time constant of CR circuit.