In a step up transformer, the turn ratio is 3 : 2. A battery of EMF 4.5V is connected across the primary windings of transformer. The voltage developed in the secondary would be:

Options

A. 4.5V
B. 30V
C. 1.5V
D. Zero

Answer

To solve the problem of finding the voltage developed in the secondary winding of a step-up transformer with a turn ratio of 3:2 when a battery of EMF 4.5V is connected across the primary winding, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Transformer Basics**: A transformer works on the principle of electromagnetic induction and is designed to operate with alternating current (AC). The primary winding receives the input voltage, and the secondary winding provides the output voltage based on the turn ratio.

2. **Identify the Turn Ratio**: The turn ratio of the transformer is given as 3:2. This means that for every 3 turns in the primary winding, there are 2 turns in the secondary winding. We can denote:
- \( n_1 = 3 \) (number of turns in the primary)
- \( n_2 = 2 \) (number of turns in the secondary)

3. **Apply the Transformer Voltage Ratio Formula**: The voltage ratio in a transformer is given by the formula:
\[ \frac{V_1}{V_2} = \frac{n_1}{n_2} \]
where \( V_1 \) is the primary voltage and \( V_2 \) is the secondary voltage.

4. **Substitute Known Values**: We know the primary voltage \( V_1 = 4.5V \) (the EMF of the battery). Substituting the values into the formula gives:
\[ \frac{4.5V}{V_2} = \frac{3}{2} \]

5. **Cross-Multiply to Solve for \( V_2 \)**:
\[ 4.5V \cdot 2 = 3 \cdot V_2 \]
\[ 9V = 3 \cdot V_2 \]

6. **Isolate \( V_2 \)**:
\[ V_2 = \frac{9V}{3} = 3V \]

7. **Conclusion**: The voltage developed in the secondary winding would be 3V.

### Final Answer:
The voltage developed in the secondary winding of the transformer is **3V**.