Practice portal › Alternating Current › AC Through R, L and C

The dimensions of RC are the same as the dimensions of which of the following?

Asked in GUJCET 2007 · Units and dimensions

Answer: (4) L/R

Step-by-step solution

Given: R resistance, L inductance, C capacitance.

Idea: in a charging R-C circuit, q=q₀(1-e^-t/RC). An exponent can only be a pure number, so RC must have the dimension of time.

The same argument on an L-R circuit, i=i₀(1-e^-Rt/L), makes L/R a time as well.

Check it directly: [R]=M¹L²T⁻³A⁻² and [L]=M¹L²T⁻²A⁻², so ([L])/([R])=T¹.

So RC and L/R share the dimension of time.

Why the other options are wrong

More AC Through R, L and C questionsAll AC Through R, L and C questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer