Which of the following dimensions will be the same as that of time?

Options

A. `L/R`
B. `C/L`
C. LC
D. `R/L`

Answer

To determine which of the following dimensions will be the same as that of time, we can analyze each option using known physical relationships and formulas.

### Step-by-Step Solution:

1. **Identify the Dimension of Time**:
- The dimension of time (T) is represented as [T].

2. **Evaluate Option 1: L/R**:
- In the context of an LR circuit, the time constant (τ) is given by τ = L/R, where L is inductance and R is resistance.
- The dimension of inductance (L) is [M^1 L^2 T^-2 A^-2] and the dimension of resistance (R) is [M^1 L^2 T^-3 A^-2].
- Therefore, the dimension of τ = L/R = [M^1 L^2 T^-2 A^-2] / [M^1 L^2 T^-3 A^-2] = [T].
- Hence, the dimension of L/R is the same as that of time.

3. **Evaluate Option 2: C/L**:
- The dimension of capacitance (C) is [M^-1 L^-2 T^4 A^2].
- The dimension of inductance (L) is [M^1 L^2 T^-2 A^-2].
- Therefore, the dimension of C/L = [M^-1 L^-2 T^4 A^2] / [M^1 L^2 T^-2 A^-2] = [M^-2 L^-4 T^6 A^4].
- This is not the same as the dimension of time.

4. **Evaluate Option 3: L*C**:
- The dimension of L*C = [M^1 L^2 T^-2 A^-2] * [M^-1 L^-2 T^4 A^2] = [M^0 L^0 T^2 A^0] = [T^2].
- This is not the same as the dimension of time.

5. **Evaluate Option 4: 1/(RC)**:
- The dimension of RC = [M^1 L^2 T^-3 A^-2] * [M^-1 L^-2 T^4 A^2] = [M^0 L^0 T^1 A^0] = [T].
- Therefore, the dimension of 1/(RC) = [T]^-1, which is not the same as the dimension of time.

### Conclusion:
From the analysis, we find that the only option that has the same dimension as time is **Option 1: L/R**.