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 answer is represented by the first option (Option 1).

To understand why this is the correct configuration of voltage polarities in a single-phase two-winding transformer, we can analyze the relationships between the terminal voltages and the induced electromotive forces (EMFs) on both the primary and secondary sides:

1. Primary Side Voltage and Induced EMF:
On the primary side, the applied terminal voltage is $V_p$ and the induced primary EMF is $E_p$. Under open-circuit (no-load) conditions, if we neglect the winding resistance and leakage reactance of the primary winding, the terminal voltage is balanced by the self-induced EMF. That is:
$V_p=E_p$
Therefore, the reference polarity of the applied primary voltage $V_p$ and the induced primary EMF $E_p$ must be the same (positive at the top terminal and negative at the bottom terminal).

2. Secondary Side Voltage and Induced EMF:
On the secondary side, $E_s$ is the mutually induced EMF in the secondary winding, and $V_s$ is the open-circuit secondary terminal voltage. Since the secondary circuit is open and no current flows, there is no voltage drop across the secondary winding resistance or leakage reactance. Thus, the terminal voltage is directly equal to the induced EMF:
$V_s=E_s$
As a result, $V_s$ and $E_s$ must share the identical polarity configuration (positive at the top terminal and negative at the bottom terminal).

3. Analysis of Winding Directions:
By inspecting the winding wraps on the magnetic core:
- The primary winding on the left limb starts at the top terminal and wraps over the front of the core.
- The secondary winding on the right limb starts at the top terminal and wraps behind the core.
- According to Lenz's law and Faraday's law of electromagnetic induction, this physical configuration of the windings determines the relative polarities of the induced voltages. The polarity arrangement shown in Option 1 correctly satisfies the electromagnetic equations where all voltages ($V_p$, $E_p$, $E_s$, and $V_s$) are in phase and share positive terminals at the top and negative terminals at the bottom.