Chapter 7.3, Problem 15PP

To determine

To calculate: the input voltage of the transformer.

Answer to Problem 15PP

The input voltage of the transformer is $\underset{\_}{60\text{ V}}$ .

Explanation of Solution

Given data:

Number of turns in primary coil, $N_1=90$

Number of turns in secondary coil, $N_2=9$

Output voltage, $V_{out}=6\text{ V}$

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,

  $\begin{array}{l}{N}_1=90\\ N_2=9\\ V_{out}=6\text{ V}\end{array}$

Substitute the values of output voltage and the number of turns in primary and secondary coils in the rearranged transformer voltage equation to get input voltage:

  $\begin{array}{l}\frac{V_{out}}{V_{in}}=\frac{N_2}{N_1}\\ V_{in}=\frac{N_1}{N_2}\times V_{out}\\ V_{in}=\left(\frac{90}{9}\right)(6\text{ V)}\\ V_{in}=(10)(6)=60\text{ V}\end{array}$

Conclusion:

The input voltage of the transformer is $\underset{\_}{60\text{ V}}$ .