In an LCR circuit, which of the following expression has the dimension of frequency:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{1}{\sqrt{LC}} \)
In an LCR circuit the natural (resonant) angular frequency is \( \omega_0 = 1/\sqrt{LC} \). Its dimension can be checked from the energy stored: the energy in an inductor is \( \frac{1}{2}LI^{2} \) and in a capacitor \( \frac{1}{2}CV^{2} \), and the time constants are \( L/R \) and \( RC \).
\( \displaystyle [L] = \frac{[V][T]}{[I]},\quad [C] = \frac{[I][T]}{[V]} \Rightarrow [LC] = [T^{2}] \)
\( \displaystyle \left[\frac{1}{\sqrt{LC}}\right] = [T^{-1}] \)
which is the dimension of frequency.
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Resonance – “… This frequency is called the resonant frequency:
\( \displaystyle \omega_0 = \frac{1}{\sqrt{LC}} \qquad (7.28) \)”