Match the following
`{:(,,"Table-1",,"Table-2"),(,(A),L,(P),[M^(0)L^(0)T^(-2)]),(,(B),"Magnetic Flux",(Q),[ML^(2)T^(-2)A^(-1)]),(,(C),LC,(R),[ML^(2)T^(-2)A^(-2)]),(,(D),CR^(2),(S),"None"):}`

Answer

To solve the problem of matching the items from Table-1 with Table-2, we need to analyze each item in Table-1 and determine its dimensional formula.

### Step-by-Step Solution:

1. **Identify the Dimensional Formula for Self-Inductance (L)**:
- The formula for the electromotive force (EMF) across an inductor is given by \( \text{EMF} = L \frac{di}{dt} \).
- Rearranging gives \( L = \frac{\text{EMF} \cdot dt}{di} \).
- EMF can be expressed as voltage, which is work done per unit charge: \( \text{EMF} = \frac{W}{Q} \).
- Therefore, \( L = \frac{W \cdot dt}{Q \cdot di} \).
- The dimensions of work done (W) are \( [ML^2T^{-2}] \), charge (Q) is \( [IT] \), and current (I) is \( [A] \).
- Thus, \( L \) can be expressed as:
\[ L = \frac{[ML^2T^{-2}] \cdot [T]}{[IT] \cdot [I]} = [ML^2T^{-2}A^{-2}] \]
- Therefore, **(A) L matches with (R)**.

2. **Identify the Dimensional Formula for Magnetic Flux (Φ)**:
- Magnetic flux can be expressed as \( Φ = L \cdot I \).
- From the previous calculation, we know \( L \) has dimensions \( [ML^2T^{-2}A^{-2}] \).
- Therefore, the dimensions of magnetic flux are:
\[ Φ = [ML^2T^{-2}A^{-2}] \cdot [A] = [ML^2T^{-2}A^{-1}] \]
- Thus, **(B) Magnetic Flux matches with (Q)**.

3. **Identify the Dimensional Formula for LC**:
- The relationship between angular frequency (ω) and inductance (L) and capacitance (C) is given by \( ω = \frac{1}{\sqrt{LC}} \).
- Rearranging gives \( LC = \frac{1}{ω^2} \).
- The dimensions of angular frequency \( ω \) are \( [T^{-1}] \), so:
\[ ω^2 = [T^{-2}] \implies LC = [T^{2}] \]
- Therefore, **(C) LC matches with (S)**.

4. **Identify the Dimensional Formula for CR²**:
- The time constant \( τ \) for an RC circuit is given by \( τ = RC \).
- The dimensions of capacitance (C) are \( [C] = [Q/V] \) where \( V = [ML^2T^{-2}A^{-1}] \).
- Thus, \( C = \frac{[IT]}{[ML^2T^{-2}A^{-1}]} = [M^{-1}L^{-2}T^{3}A^{2}] \).
- Therefore, the dimensions of \( CR^2 \) can be calculated as:
\[ CR^2 = [M^{-1}L^{-2}T^{3}A^{2}] \cdot [T] = [M^{-1}L^{-2}T^{4}A^{2}] \]
- Since this does not match any specific option, we conclude that **(D) CR² matches with (S)**.

### Final Matches:
- (A) L matches with (R)
- (B) Magnetic Flux matches with (Q)
- (C) LC matches with (S)
- (D) CR² matches with (S)