If `C,R,L` and `I` denot capacity resitance, inductance and electric current respecitively, the quantities having the same dimensions of time are
(a) `CR`, (b) `L//R`, (c) `sqrt(L//C)`, (d) `LI^(2)`

Options

A. (1) and (2) only
B. (1) and (3) only
C. (1) and (4) only
D. (1), (2) and (3) only

Answer

To solve the problem, we need to find which of the given quantities have the same dimensions as time (T). We will analyze each option step-by-step.

### Step 1: Write down the dimensions of the given quantities.
1. **Capacitance (C)**: The dimensional formula for capacitance is:
\[ [C] = M^{-1} L^{-2} T^{4} I^{2} \]

2. **Resistance (R)**: The dimensional formula for resistance is:
\[ [R] = M L^{2} I^{-2} T^{-3} \]

3. **Inductance (L)**: The dimensional formula for inductance is:
\[ [L] = M L^{2} I^{-2} T^{-2} \]

4. **Electric Current (I)**: The dimensional formula for electric current is:
\[ [I] = I \]

### Step 2: Analyze each option to find their dimensions.

#### Option (a): \( CR \)
\[ [CR] = [C] \times [R] = (M^{-1} L^{-2} T^{4} I^{2}) \times (M L^{2} I^{-2} T^{-3}) \]
Calculating this gives:
\[ [CR] = M^{0} L^{0} T^{1} I^{0} = T \]
Thus, \( CR \) has the dimension of time.

#### Option (b): \( \frac{L}{R} \)
\[ \left[\frac{L}{R}\right] = \frac{[L]}{[R]} = \frac{M L^{2} I^{-2} T^{-2}}{M L^{2} I^{-2} T^{-3}} = T \]
Thus, \( \frac{L}{R} \) also has the dimension of time.

#### Option (c): \( \sqrt{\frac{L}{C}} \)
\[ \left[\sqrt{\frac{L}{C}}\right] = \sqrt{\frac{[L]}{[C]}} = \sqrt{\frac{M L^{2} I^{-2} T^{-2}}{M^{-1} L^{-2} T^{4} I^{2}}} \]
Calculating this gives:
\[ = \sqrt{M^{1} L^{4} I^{-4} T^{-6}} = M^{\frac{1}{2}} L^{2} I^{-2} T^{-3} \]
This does not simplify to time.

#### Option (d): \( LI^{2} \)
\[ [LI^{2}] = [L] \times [I^{2}] = (M L^{2} I^{-2} T^{-2}) \times (I^{2}) = M L^{2} T^{-2} \]
This does not simplify to time.

### Conclusion
From the analysis:
- Option (a) \( CR \) has dimensions of time.
- Option (b) \( \frac{L}{R} \) has dimensions of time.
- Option (c) \( \sqrt{\frac{L}{C}} \) does not have dimensions of time.
- Option (d) \( LI^{2} \) does not have dimensions of time.

Thus, the quantities that have the same dimensions as time are:
**(a) and (b)**.

### Final Answer
The correct options are (a) and (b).

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