L, C and R represent the physical quantities, inductance, capacitance and resistance respectively. The combination(s) which have the dimensions of frequency are

Options

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

Explanation

To determine which combinations of inductance (L), capacitance (C), and resistance (R) have the dimensions of frequency, we first need to establish the dimensional formulas for each of these quantities.

### Step 1: Write down the dimensions of R, C, and L.

- **Resistance (R)**:
\[ [R] = M^1 L^2 T^{-3} A^{-2} \]

- **Capacitance (C)**:
\[ [C] = M^{-1} L^{-2} T^{-4} A^2 \]

- **Inductance (L)**:
\[ [L] = M^1 L^2 T^{-2} A^{-2} \]

### Step 2: Analyze the combinations given in the question.

We will analyze each combination (A, B, C, D) to see if they yield the dimensions of frequency, which is represented as \( [\text{Frequency}] = T^{-1} \).

#### Combination A: \( \frac{1}{RC} \)

\[ RC = R \times C = (M^1 L^2 T^{-3} A^{-2}) \times (M^{-1} L^{-2} T^{-4} A^2) \]

Calculating the dimensions:

\[ RC = M^{1-1} L^{2-2} T^{-3-4} A^{-2+2} = M^0 L^0 T^{-7} A^0 = T^{-7} \]

Thus,

\[ \frac{1}{RC} = T^{7} \]

This does not represent frequency.

#### Combination B: \( \frac{R}{L} \)

\[ \frac{R}{L} = \frac{M^1 L^2 T^{-3} A^{-2}}{M^1 L^2 T^{-2} A^{-2}} = M^{1-1} L^{2-2} T^{-3+2} A^{-2+2} = M^0 L^0 T^{-1} A^0 = T^{-1} \]

This represents frequency.

#### Combination C: \( \frac{1}{\sqrt{LC}} \)

\[ LC = L \times C = (M^1 L^2 T^{-2} A^{-2}) \times (M^{-1} L^{-2} T^{-4} A^2) \]

Calculating the dimensions:

\[ LC = M^{1-1} L^{2-2} T^{-2-4} A^{-2+2} = M^0 L^0 T^{-6} A^0 = T^{-6} \]

Thus,

\[ \frac{1}{\sqrt{LC}} = \frac{1}{T^{-3}} = T^{3} \]

This does not represent frequency.

#### Combination D: \( \frac{C}{L} \)

\[ \frac{C}{L} = \frac{M^{-1} L^{-2} T^{-4} A^2}{M^1 L^2 T^{-2} A^{-2}} = M^{-1-1} L^{-2-2} T^{-4+2} A^{2+2} = M^{-2} L^{-4} T^{-2} A^{4} \]

This does not represent frequency.

### Conclusion

The only combination that represents frequency is **B**. Therefore, the correct answer is:

- **B: \( \frac{R}{L} \)** represents the dimensions of frequency.