If L, C and R are the self inductance m capacitance and resistance respectively which of the following does not have the dimension of time ?

Options

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

Explanation

To solve the problem, we need to analyze the dimensions of the quantities involved: self-inductance (L), capacitance (C), and resistance (R). We will determine which of the combinations of these quantities does not have the dimension of time.

### Step-by-Step Solution:

1. **Identify the dimensions of L, C, and R:**
- Self-inductance (L) has the dimension of \([M^1 L^2 T^{-2} A^{-2}]\).
- Capacitance (C) has the dimension of \([M^{-1} L^{-2} T^4 A^2]\).
- Resistance (R) has the dimension of \([M^1 L^2 T^{-3} A^{-2}]\).

2. **Calculate the dimensions of RC:**
- The dimension of \(RC\) is:
\[ [R] \cdot [C] = [M^1 L^2 T^{-3} A^{-2}] \cdot [M^{-1} L^{-2} T^4 A^2] \]
- Simplifying this gives:
\[ = [M^{1-1} L^{2-2} T^{-3+4} A^{-2+2}] = [T^1] \]
- Therefore, \(RC\) has the dimension of time.

3. **Calculate the dimensions of L/R:**
- The dimension of \(L/R\) is:
\[ [L] / [R] = [M^1 L^2 T^{-2} A^{-2}] / [M^1 L^2 T^{-3} A^{-2}] \]
- Simplifying this gives:
\[ = [M^{1-1} L^{2-2} T^{-2+3} A^{-2+2}] = [T^1] \]
- Therefore, \(L/R\) also has the dimension of time.

4. **Calculate the dimensions of \(\sqrt{LC}\):**
- The dimension of \(\sqrt{LC}\) is:
\[ \sqrt{[L] \cdot [C]} = \sqrt{[M^1 L^2 T^{-2} A^{-2}] \cdot [M^{-1} L^{-2} T^4 A^2]} \]
- Simplifying this gives:
\[ = \sqrt{[M^{1-1} L^{2-2} T^{-2+4} A^{-2+2}]} = \sqrt{[T^2]} = [T^1] \]
- Therefore, \(\sqrt{LC}\) has the dimension of time.

5. **Calculate the dimensions of L/C:**
- The dimension of \(L/C\) is:
\[ [L] / [C] = [M^1 L^2 T^{-2} A^{-2}] / [M^{-1} L^{-2} T^4 A^2] \]
- Simplifying this gives:
\[ = [M^{1+1} L^{2+2} T^{-2-4} A^{-2-2}] = [M^2 L^4 T^{-6} A^{-4}] \]
- Therefore, \(L/C\) does not have the dimension of time.

### Conclusion:
The quantity that does not have the dimension of time is \(L/C\).