Question
L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
✓
Answer
- $\frac{1}{\text{RC}}$
- $\frac{\text{R}}{\text{L}}$
- $\frac{1}{\sqrt{\text{LC}}}$
þ Time constant t = RC in RC circuit
frequency $=\frac{1}{\tau}=\frac{1}{\text{RC}} \ ...(\text{i})$
þ Time constant in LR circuit is $\tau=\frac{\text{L}}{\text{RC}}$
frequency $\frac{1}{\tau}=\frac{\text{R}}{\text{L}} \ ...(\text{ii})$
þ eq. (i) & (ii) multiply
frequency $=\frac{1}{\text{LC}}$
frequency $=\frac{1}{\sqrt{2\text{C}}}$
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