Electromotive force and Electric potential differ in the dimensions of

Options

A. Mass
B. Length
C. Electric current
D. None of the above

Answer

To solve the question regarding the difference in dimensions between electromotive force (emf) and electric potential, we can follow these steps:

### Step 1: Understand the Definitions
- **Electromotive Force (emf)**: It is defined as the energy provided per unit charge by a source of electrical energy (like a battery).
- **Electric Potential**: It is the amount of electric potential energy per unit charge at a point in an electric field.

### Step 2: Identify the Formula
Both electromotive force and electric potential can be expressed using the same formula:
\[ \text{emf} = V = \frac{W}{Q} \]
Where:
- \( W \) = Work done (in joules)
- \( Q \) = Charge (in coulombs)

### Step 3: Determine the Dimensions
- The dimension of work \( W \) is given by:
\[ [W] = [M L^2 T^{-2}] \]
- The dimension of charge \( Q \) is given by:
\[ [Q] = [I T] \]
- Therefore, the dimension of electric potential (and emf) can be calculated as follows:
\[ [V] = \frac{[W]}{[Q]} = \frac{[M L^2 T^{-2}]}{[I T]} = [M L^2 T^{-3} I^{-1}] \]

### Step 4: Conclusion
Since both electromotive force and electric potential have the same dimensional formula, we conclude that they do not differ in dimensions.

### Final Answer
The answer is that electromotive force and electric potential have the same dimensions.