Chapter SH, Problem 7.7APP

To determine

To calculate: Number of turns in the primary coil of a step-down transformer.

Answer to Problem 7.7APP

The number of turns in the primary coil of a step-down transformer is $\underset{\_}{320}$ .

Explanation of Solution

Given:

Input voltage = $400\text{ V}$

Output voltage = $100\text{ V}$

Number of turns in the secondary coil = $80$

Formula used:

Transformer voltage equation is given by,

$\frac{V_{\text{out}}}{V_{\text{in}}}=\frac{N_2}{N_1}$

Where $V_{\text{out}}$ is the output voltage, $V_{\text{in}}$ is the input voltage, $N_2$ is the number of turns in the secondary coil and $N_1$ is the number of turns in the primary coil.

Calculation:

The number of turns in the primary coil is calculated as:

$\begin{array}{l}\frac{V_{\text{out}}}{V_{\text{in}}}=\frac{N_2}{N_1}\\ N_1=\frac{V_{\text{in}}\cdot N_2}{V_{\text{out}}}\\ N_1=\frac{\left(400\text{ V}\right)\cdot \left(80\right)}{\text{100 V}}\\ N_1=320\end{array}$

Conclusion:

The number of turns in the primary coil of a step-down transformer is $\underset{\_}{320}$ .