Chapter 7, Problem 49R

To determine

To calculate: the ratio of the number of turns in primary coil to the number of turns in the secondary coil of the transformer.

Answer to Problem 49R

The ratio of number of turns in primary coil to the number of turns in the secondary coil of the transformer is $\underset{\_}{1:1000}$ .

Explanation of Solution

Given data:

Input voltage, $V_{in}=12\text{ V}$

Output voltage, $V_{out}=12000\text{ V}$

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,

  $\begin{array}{l}{V}_{in}=12\text{ V}\\ V_{out}=12000\text{ V}\end{array}$

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

  $\begin{array}{l}\frac{V_{out}}{V_{in}}=\frac{N_2}{N_1}\\ \frac{N_1}{N_2}=\frac{V_{in}}{V_{out}}\\ \frac{N_1}{N_2}=\frac{12\text{ V}}{12000\text{ V}}\\ \frac{N_1}{N_2}=\frac{1}{1000}\end{array}$

Conclusion:

The ratio of turns in primary coil to the turns in the secondary coil of the transformer is $\underset{\_}{1:1000}$ .