Electricity generated in power plants travels through power lines on its way to homes and businesses. A major issue of providing electricity is that the voltage in power lines is often 500 kV, many orders of magnitude greater than the voltage that common household appliances run on (120 V). To rectify this disparity in electrical potentials, transformers are utilized to ‘step down’ voltage. A basic transformer functions through two coupled, coiled conductors, referred to as the ‘primary’ and ‘secondary’ coils. A change in the primary current creates a varying magnetic field in the secondary coil which, in turn, results in a voltage in the secondary coil. The overall schematic of a transformer is as follows:

Figure 1. Transformer Schematic.

Where V_P is the voltage across the primary coil and V_S is the induced voltage caused through current change in the primary coil. N_P refers to the number of coils in the primary conductor and N_S refers to the number of coils in the secondary conductor. I_P and I_S refer to the respective currents for the primary and secondary coils. The relationship between these variables is expressed through the following expression:

The above equation holds for ideal transformers, in which the power in the primary conductor is equivalent to the power in the secondary conductor, i.e. there is no energy loss during the processing of the transformer. This similar set up can also be used to ‘step up’ voltage if a particular system requires such functionality.
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