The dimension of the ratio of magnetic flux and the resistance is equal to that of:

Options

A. emf
B. chare
C. inductance
D. current

Answer

To solve the problem of finding the dimension of the ratio of magnetic flux to resistance, we will follow these steps:

### Step 1: Determine the Dimension of Magnetic Flux
The magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass. The dimension of magnetic flux is given by:
\[ \text{Dimension of Magnetic Flux} = [\Phi] = M L^2 T^{-2} A^{-1} \]

### Step 2: Determine the Dimension of Resistance
The resistance (R) is defined by Ohm's law, where resistance is the ratio of voltage (V) to current (I). The dimension of resistance is given by:
\[ \text{Dimension of Resistance} = [R] = M L^2 T^{-3} A^{-2} \]

### Step 3: Calculate the Ratio of Magnetic Flux to Resistance
Now, we need to find the dimension of the ratio of magnetic flux to resistance:
\[ \frac{\text{Magnetic Flux}}{\text{Resistance}} = \frac{[Φ]}{[R]} = \frac{M L^2 T^{-2} A^{-1}}{M L^2 T^{-3} A^{-2}} \]

### Step 4: Simplify the Expression
When we divide the dimensions, we can cancel out the common terms:
\[ = \frac{M L^2 T^{-2} A^{-1}}{M L^2 T^{-3} A^{-2}} = \frac{1}{1} \cdot \frac{T^{-2}}{T^{-3}} \cdot \frac{A^{-1}}{A^{-2}} = T^{1} A^{1} \]
Thus, the dimension simplifies to:
\[ = T^1 A^1 = T A \]

### Conclusion
The dimension of the ratio of magnetic flux to resistance is equal to that of charge, which can be expressed as:
\[ \text{Dimension of Charge} = [Q] = T^1 A^1 \]