why do we use a center tap at the secondary coil of a tranformer ?
There are a number or multiple winding transformers available which have two primary windings of identical voltage and current ratings and two secondary windings also with identical voltage and current ratings. These transformers are designed so that they can be used in a variety of applications with the windings connected together in either a series or parallel combinations for higher primary voltages or secondary currents. These types of multiple winding transformers are more commonly called Dual Voltage Transformers as shown.
Dual Primary & Dual Secondary Transformer.
Another type of dual voltage transformer which has only one secondary winding that is "tapped" at its electrical center point is called the Center-tap Transformer.
Center Tapped Transformers
A center-tap transformer is designed to provide two separate secondary voltages, VA and VB with a common connection. This type of transformer configuration produces a two-phase, 3-wire supply. The secondary voltages are the same and proportional to the supply voltage, VP, therefore power in each winding is the same. The voltages produced across each of the secondary winding is determined by the turns ratio as shown.
Above shows a typical center-tap transformer. The tapping point is in the exact center of the secondary winding providing a common connection for two equal but opposite secondary voltages. With the center-tap grounded, the output VA will be positive in nature with respect to the ground, while the voltage at the other secondary, VB will be negative and opposite in nature, that is they are 180o electrical degrees out-of-phase with each other. However, there is one disadvantage of using an un-grounded center tapped transformer and that is it can produce unbalanced voltages in the two secondary windings due to unsymmetrical currents flowing in the common third connection because of unbalanced loads.