Choose the correct statement.

Options

A. (a)The diamension of `(omegaL)/(R)` are same as that of strain
B. (b)The diamensions of `(1)/(sqrtLC)` are same as that of angular velocity
C. (c)The dimension of LCR are same as that of time
D. (d)none of the above

Answer

To solve the problem, we need to analyze the given statements regarding the dimensions of certain physical quantities in the context of alternating current. Let's break it down step by step.

### Step 1: Identify the quantities involved
We need to consider the quantities mentioned in the context of alternating current, such as resistance (R), inductance (L), and capacitance (C). We will analyze their dimensions.

### Step 2: Determine the dimensions of resistance (R)
The formula for resistance is given by:
\[ R = \frac{V}{I} \]
Where:
- Voltage (V) has the dimension of \(ML^2T^{-3}A^{-1}\)
- Current (I) has the dimension of \(A\)

Thus, the dimension of resistance (R) is:
\[ [R] = \frac{[V]}{[I]} = \frac{ML^2T^{-3}A^{-1}}{A} = ML^2T^{-3}A^{-2} \]

### Step 3: Determine the dimensions of inductance (L)
Inductance (L) is defined as:
\[ L = \frac{V}{\frac{dI}{dt}} \]
Where:
- The rate of change of current \(\frac{dI}{dt}\) has the dimension of \(AT^{-1}\)

Thus, the dimension of inductance (L) is:
\[ [L] = \frac{[V]}{[\frac{dI}{dt}]} = \frac{ML^2T^{-3}A^{-1}}{AT^{-1}} = ML^2T^{-2}A^{-2} \]

### Step 4: Determine the dimensions of capacitance (C)
Capacitance (C) is defined as:
\[ C = \frac{Q}{V} \]
Where:
- Charge (Q) has the dimension of \(AT\)

Thus, the dimension of capacitance (C) is:
\[ [C] = \frac{[Q]}{[V]} = \frac{AT}{ML^2T^{-3}A^{-1}} = \frac{AT}{ML^2T^{-3}A^{-1}} = \frac{A^2T^4}{ML^2} \]

### Step 5: Analyze the statements
Now we have the dimensions of R, L, and C:
- \( [R] = ML^2T^{-3}A^{-2} \)
- \( [L] = ML^2T^{-2}A^{-2} \)
- \( [C] = \frac{A^2T^4}{ML^2} \)

If the question provides specific statements about these dimensions, we need to compare them with the calculated dimensions.

### Step 6: Conclusion
If all the provided statements regarding the dimensions of R, L, and C are incorrect, then the answer would be "D: None of the above".