Chapter 37, Problem 55A

A transformer has an input of 9 volts and an output of 36 volts. If the input is changed to 12 volts, show that the output would be 48 volts.

To determine

To Show: the output is $48volts$ for the given information in a transformer

Answer to Problem 55A

The output voltage is $48volts$

Explanation of Solution

Given:

Transformer output voltage $\left(V_2\right)=36V$

Transformer input voltage $\left(V_1\right)=9V$

Changed input voltage $\left(V_1\right)=12V$

Formula used:

  $\frac{V_1}{V_2}=C$

Calculation:

The transformer voltage remains constant. Assuming no losses in the transformer and input voltage is proportional to output voltage.

Considering the concept of transformer voltage remains constant.

  $\frac{V_1}{V_2}=C$

Equation becomes,

  ${\left(\frac{V_1}{V_2}\right)}_{input}={\left(\frac{V_1}{V_2}\right)}_{output}$

  $\begin{array}{l}\left(\frac{9}{12}\right)=\left(\frac{36}{V_2}\right)\\ V_2=48.\end{array}$

Hence, proved

Conclusion:  Considering the voltage ratio in the transformer the voltage is $48volts$ , hence proved.