Chapter 37, Problem 56A

A model electric train requires a low voltage to operate. If the primary coil of its transformer has 400 turns, and the secondary has 40 turns, how many volts will power the train when the primary is connected to a 120-volt household circuit?

To determine

To calculate: the voltage of a train in a transformer for given information

Answer to Problem 56A

The voltage on secondary coil is $12V.$

Explanation of Solution

Given:

Primary coil $\left(N_1\right)=400turns$

Secondary coil $\left(N_2\right)=40turns$

Voltage on primary winding $\left(V_1\right)=120volts$

Formula used:

  $\frac{V_1}{V_2}=\frac{N_1}{N_2}$ .

Calculation:

The relation between voltage and number on turns on primary and secondary coil is,

  $\frac{V_1}{V_2}=\frac{N_1}{N_2}$

The equation becomes

  $\begin{array}{l}{V}_2=V_1\frac{N_2}{N_1}\\ V_2=120\times \frac{40}{400}\\ =12volts\end{array}$

The voltage on secondary winding is $12V.$

Conclusion: 

From a relation between the number of turns and the voltage ratio, the voltage on secondary coil is calculated as $12V.$