Question

Dimensions of $ \frac{L}{RCV} $ are

• A. $ [A^{-1}] $
• B. $ [A^{-2}] $
• C. $ [A] $
• D. $ [{{A}^{2}}] $

Answer 1

The Correct Option is A

\(\frac{L}{R}\) has the dimensions of time. Because \(\frac{L}{R}\) is the time constant of \(L-R\) circuit. 
\(\therefore \left[\frac{L}{R}\right]=[ T ]\) 
Charge \(=\) Capacitance \(\times\) Potential difference 
\(Q=C V\) 
and \({[Q]=[A T]}\)
\(\therefore \left[\frac{L}{R C V}\right]=\left[\frac{L}{Q}\right]\)
\(=\left[\frac{T}{A T}\right]\)
\(\left[\frac{L}{R C V}\right]=\left[A^{-1}\right]\)

Therefore, the correct option is (A): \([A^{-1}]\)