If `L,C` and `R` represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency

Options

A. `(1)/(RC)`
B. `(R )/(L)`
C. `(1)/(sqrt(LC))`
D. `(C )/(L)`

Answer

To solve the problem, we need to analyze the dimensions of resistance (R), inductance (L), and capacitance (C) and check which of the given options does not represent the dimensions of frequency.

### Step-by-Step Solution:

1. **Identify the Dimensions of R, L, and C:**
- The dimension of resistance (R) is given by:
\[ [R] = M L^2 T^{-3} A^{-2} \]
- The dimension of inductance (L) is given by:
\[ [L] = M L^2 T^{-2} A^{-2} \]
- The dimension of capacitance (C) is given by:
\[ [C] = M^{-1} L^{-2} T^4 A^2 \]

2. **Evaluate Each Option:**
- **Option A: \( \frac{1}{RC} \)**
\[ [RC] = [R][C] = (M L^2 T^{-3} A^{-2})(M^{-1} L^{-2} T^4 A^2) \]
Simplifying:
\[ = M^{1-1} L^{2-2} T^{-3+4} A^{-2+2} = T^1 = T \]
Thus,
\[ \frac{1}{RC} \Rightarrow [\frac{1}{RC}] = T^{-1} \]
This represents frequency.

- **Option B: \( \frac{R}{L} \)**
\[ [\frac{R}{L}] = \frac{[R]}{[L]} = \frac{M L^2 T^{-3} A^{-2}}{M L^2 T^{-2} A^{-2}} \]
Simplifying:
\[ = M^{1-1} L^{2-2} T^{-3+2} A^{-2+2} = T^{-1} \]
This also represents frequency.

- **Option C: \( \frac{1}{\sqrt{LC}} \)**
\[ [\sqrt{LC}] = \sqrt{[L][C]} = \sqrt{(M L^2 T^{-2} A^{-2})(M^{-1} L^{-2} T^4 A^2)} \]
Simplifying:
\[ = \sqrt{M^{1-1} L^{2-2} T^{-2+4} A^{-2+2}} = \sqrt{T^2} = T \]
Thus,
\[ \frac{1}{\sqrt{LC}} \Rightarrow [\frac{1}{\sqrt{LC}}] = T^{-1} \]
This represents frequency.

- **Option D: \( \frac{C}{L} \)**
\[ [\frac{C}{L}] = \frac{[C]}{[L]} = \frac{M^{-1} L^{-2} T^4 A^2}{M L^2 T^{-2} A^{-2}} \]
Simplifying:
\[ = M^{-1-1} L^{-2-2} T^{4+2} A^{2+2} = M^{-2} L^{-4} T^6 A^4 \]
This does not represent the dimension of frequency.

3. **Conclusion:**
The option that does not represent the dimensions of frequency is:
\[ \text{Option D: } \frac{C}{L} \]

### Final Answer:
**Option D does not represent the dimension of frequency.**