Dimensional formula for electromotive force is same as that for

Options

A. potential
B. current
C. force
D. energy

Answer

To find the dimensional formula for electromotive force (EMF), we start by understanding its definition and relation to other physical quantities.

### Step 1: Definition of Electromotive Force (EMF)
Electromotive force (EMF) is defined as the work done per unit charge. Mathematically, it can be expressed as:
\[ \text{EMF} = \frac{\text{Work done}}{\text{Charge}} \]

### Step 2: Dimensional Formula for Work Done
Work done (W) is defined as the product of force (F) and displacement (s). The dimensional formula for force is given by:
\[ [F] = [M][L][T^{-2}] \]
where:
- \(M\) = mass
- \(L\) = length
- \(T\) = time

Thus, the dimensional formula for work done is:
\[ [W] = [F][s] = [M][L][T^{-2}][L] = [M][L^2][T^{-2}] \]

### Step 3: Dimensional Formula for Charge
The dimensional formula for electric charge (Q) is:
\[ [Q] = [I][T] \]
where \(I\) is the current.

### Step 4: Combining the Dimensional Formulas
Now, substituting the dimensional formulas of work done and charge into the expression for EMF:
\[ [\text{EMF}] = \frac{[W]}{[Q]} = \frac{[M][L^2][T^{-2}]}{[I][T]} = [M][L^2][T^{-3}][I^{-1}] \]

### Step 5: Comparison with Other Quantities
Now we compare the dimensional formula of EMF with the options provided:
1. **Potential**: The potential is also defined as work done per unit charge, so it has the same dimensional formula as EMF.
2. **Current**: The dimensional formula for current is \([I]\), which is not the same as EMF.
3. **Force**: The dimensional formula for force is \([M][L][T^{-2}]\), which is different from EMF.
4. **Energy**: The dimensional formula for energy is the same as work done, \([M][L^2][T^{-2}]\), which is also different from EMF.

### Conclusion
The dimensional formula for electromotive force (EMF) is the same as that for electric potential. Therefore, the correct answer is:
**Option 1: Potential**