Question

The term Z = s/u (s = distance, u = speed) is dimensionally incompatible with the term

(1) LC (L = self inductance, C = capacitance)

(2) L/R (L = self inductance, R = resistance)

(3) RC (R = resistance, C = capacitance)

(4) √(l/g) (l = length, g = acceleration)

Answer 1

(1) LC (L = self inductance, C = capacitance)

The term z(=s/u) has the dimensions of time.

Using the dimensions of

We find that the terms (L/R)  and (RC) both have the dimensions of time.

∴ This term also has the dimensions of time.

However, the term [LC] = [T²]

It, therefore, is dimensionally incompatible with the given term, i.e. Z.