Condition for step-down transformer is:

Options

A. `i_(s)=i_(p) and N_(s) = N_(p)`
B. `i_(s) = i_(p) and N_(s) = N_(p)`
C. `i_(s) lt i_(p) and N_(s) gt N_(p)`
D. `i_(s) lt i_(p) and N_(s) = N_(p)`

Explanation

To understand the condition for a step-down transformer, we need to analyze the relationship between the primary and secondary coils in terms of voltage, current, and the number of turns in each coil.

### Step-by-step solution:

1. **Definition of a Transformer**: A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of two coils: the primary coil and the secondary coil.

2. **Types of Transformers**: There are two main types of transformers: step-up transformers and step-down transformers. A step-up transformer increases voltage, while a step-down transformer decreases voltage.

3. **Understanding a Step-Down Transformer**:
- In a step-down transformer, the voltage across the secondary coil (Vs) is less than the voltage across the primary coil (Vp).
- This means that the transformer reduces the voltage from the primary to the secondary side.

4. **Relationship Between Turns and Voltage**:
- The relationship between the primary voltage (Vp), secondary voltage (Vs), primary turns (Np), and secondary turns (Ns) is given by the formula:
\[ \frac{Vp}{Vs} = \frac{Np}{Ns} \]
- For a step-down transformer, the number of turns in the secondary coil (Ns) is greater than the number of turns in the primary coil (Np). Therefore, we can say:
\[ Ns > Np \]
- This implies that:
\[ Vs < Vp \]

5. **Current Relationship**:
- According to the law of conservation of energy, the power input to the primary coil must equal the power output from the secondary coil (ignoring losses):
\[ Pp = Ps \]
- Where \( P = VI \) (Power = Voltage × Current).
- Therefore, we can express this as:
\[ Vp \cdot Ip = Vs \cdot Is \]
- Rearranging gives us:
\[ \frac{Ip}{Is} = \frac{Vs}{Vp} \]
- Since \( Vs < Vp \) in a step-down transformer, it follows that \( Is > Ip \). This means the current in the secondary coil (Is) is greater than the current in the primary coil (Ip).

### Conclusion:
In summary, the condition for a step-down transformer is characterized by:
- The number of turns in the secondary coil (Ns) is greater than the number of turns in the primary coil (Np).
- The voltage in the secondary coil (Vs) is less than the voltage in the primary coil (Vp).
- The current in the secondary coil (Is) is greater than the current in the primary coil (Ip).