Chapter 2, Problem 2.1Q

Is the turns ratio of a transformer the same as the ratio of voltages across the transformer? Why or why not?

To determine

Whether a transformer’s turns ratio is same as a transformer’s voltage ratio or not along with reason.

Explanation of Solution

Diagram of ideal transformer is:

Mutual flux of transformer is  $\varphi ={\varphi }_m\sin \omega t$

Primary voltage of transformer is  $\begin{array}{l}{V}_p\left(t\right)=N_p\frac{d\varphi }{dt}\\ V_p\left(t\right)=N_p\frac{d}{dt}\left({\varphi }_m\sin \omega t\right)\\ V_p\left(t\right)=N_p\omega {\varphi }_m\cos \omega t\end{array}$

Secondary voltage of transformer is −  $\begin{array}{l}{V}_s\left(t\right)=N_s\frac{d\varphi }{dt}\\ V_s\left(t\right)=N_s\frac{d}{dt}\left({\varphi }_m\sin \omega t\right)\\ V_s\left(t\right)=N_s\omega {\varphi }_m\cos \omega t\end{array}$

Ratio of primary and secondary voltage is  $\frac{V_p\left(t\right)}{V_s\left(t\right)}=\frac{N_p}{N_s}$

It is observed that ratio of voltages of transformer are same as ratio of their turns because flux linking both the coils is same. So, voltage will be directly proportional to number of turns.