Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here. V_p is the applied primary voltage. E_p is the induced primary voltage. V_s is the open circuit secondary voltage, and E_s is the induced secondary voltage.

The correct option representing the possible voltage polarities in a single-phase two-winding transformer is:

1. Dot Convention and Induced EMF Polarity:
According to the dot convention in transformer windings, the induced EMFs in both the primary ($E_p$) and secondary ($E_s$) windings have identical polarities at the dotted terminals relative to the non-dotted terminals at any given instant. In Option 1, the dot on the primary winding is placed at the bottom terminal, while the dot on the secondary winding is placed at the top terminal.
Looking closely at the induced EMFs ($E_p$ and $E_s$):

- For the primary side, the '+' polarity of $E_p$ is at the top terminal and the '-' polarity is at the bottom (dotted) terminal.
- For the secondary side, the '+' polarity of $E_s$ is at the top (dotted) terminal and the '-' polarity is at the bottom terminal.
Therefore, the dotted terminals consistently carry the same relative induced voltage polarity (the '-' of $E_p$ is at the bottom dot, and the '+' of $E_s$ is at the top dot, showing that both dotted terminals experience identical polarity shifts due to mutual flux).

2. Applied Primary Voltage ($V_p$) vs Induced Primary Voltage ($E_p$):
According to Lenz's Law, the induced primary electromotive force (EMF) opposes the applied primary voltage. Therefore, the polarity of $E_p$ must match the polarity of $V_p$ to act as a counter-EMF opposing the source voltage. In Option 1, both $V_p$ and $E_p$ have '+' at the top terminal and '-' at the bottom terminal.

3. Induced Secondary Voltage ($E_s$) vs Open Circuit Terminal Voltage ($V_s$):
On an open-circuit secondary side, no current flows, so the terminal voltage $V_s$ is directly equal to the induced EMF $E_s$ in both magnitude and polarity. In Option 1, both $E_s$ and $V_s$ have '+' at the top terminal and '-' at the bottom terminal.

Thus, Option 1 satisfies all physical and electromagnetic constraints for voltage polarities in a single-phase two-winding transformer.