Chapter 7.3, Problem 17PP

To determine

To calculate: the ratio of turns in primary coil to turns in the secondary coil of the step-down transformer.

Answer to Problem 17PP

The ratio of turns in primary coil to turns in the secondary coil of the step-down transformer is $\underset{\_}{\text{2000}:1}$ .

Explanation of Solution

Given data:

Input voltage, $V_{in}=240,000\text{ V}$

Output voltage, $V_{out}=120\text{ V}$ (the standard voltage for a wall socket in North America)

Formula used:

Transformer Voltage Equation:

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

Where $V_{out}$ is the output voltage of the transformer in volts, $V_{in}$ is its input voltage in volts, $N_2$ is the turns in secondary coil, and $N_1$ is the turns in primary coil.

Calculation:

As per the problem,

  $\begin{array}{l}{V}_{in}=240,000\text{ V}\\ V_{out}=120\text{ V}\end{array}$

Substitute the values of input and output voltage in therearranged transformer voltage equation to get ratio of the turns in primary coil to that in secondary coil:

  $\begin{array}{l}\frac{V_{out}}{V_{in}}=\frac{N_2}{N_1}\\ \frac{N_1}{N_2}=\frac{V_{in}}{V_{out}}\\ \frac{N_1}{N_2}=\frac{240,000\text{ V}}{120\text{ V}}\\ \frac{N_1}{N_2}=\frac{2000}{1}\end{array}$

Conclusion:

Theratio of turns in primary coil to turns in the secondary coil of the step-down transformer is $\underset{\_}{\text{2000}:1}$ .