Which is not possible for a transformer?

Options

A. `E_p I_p = E_s I_s`
B. `E_p I_p lt E_s I_s`
C. `E_p I_p gt E_s I_s`
D. all are possible

Explanation

To determine what is not possible for a transformer, we need to analyze the basic principles of how transformers operate and the concept of efficiency.

### Step-by-Step Solution:

1. **Understand the Function of a Transformer**: A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. It typically consists of two coils of wire (primary and secondary) wrapped around a magnetic core.

2. **Define Key Terms**:
- **EMF (E)**: Electromotive force, which is the voltage produced by the transformer.
- **Current (I)**: The flow of electric charge.
- **Power (P)**: The rate at which energy is transferred or converted, calculated as the product of EMF and current.

3. **Power in a Transformer**:
- The power in the primary coil (input power) is given by \( P_{input} = E_P \times I_P \).
- The power in the secondary coil (output power) is given by \( P_{output} = E_S \times I_S \).

4. **Efficiency of a Transformer**:
- The efficiency (\( \eta \)) of a transformer is defined as the ratio of output power to input power:
\[ \eta = \frac{P_{output}}{P_{input}} = \frac{E_S \times I_S}{E_P \times I_P} \]
- Efficiency is always less than or equal to 100%, meaning that no transformer can convert all input power into output power without any losses.

5. **Identify What is Not Possible**:
- Since the efficiency of a transformer cannot exceed 100%, it is impossible for a transformer to have an efficiency of 100%. This would imply that all input power is converted to output power with no losses, which is not feasible in real-world applications due to factors like heat loss, magnetic losses, etc.

### Conclusion:
The statement that is not possible for a transformer is achieving 100% efficiency.

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