What is the formula for the voltage across each field coil?

To provide a precise response, I will need to clarify the context in which you are asking about the voltage across each field coil. The voltage in such a scenario can depend on various factors including the type of machine (e.g., DC motor, AC generator), how the field coils are connected (series or parallel), and the source of excitation (external voltage source, self-excitation).

However, in a general sense for a DC machine, if we are talking about the field coils of a separately excited DC machine (a common scenario), the voltage across each field coil (V_field) is essentially determined by the external voltage source applied to the field winding. In a series connection, it can be a portion of the total applied voltage depending on the number of coils and their resistances.

In mathematical terms, for a separately excited field coil or for coils in parallel, the formula is quite straightforward:

[V_{field} = V_{applied}]

where (V_{field}) is the voltage across the field winding and (V_{applied}) is the external voltage applied to the field winding.

In a series circuit, the situation gets more complex as the same current flows through all components in series, but the voltage drop across each component (field coil, in this case) will vary based on the resistance of each component. If the field coils have equal resistance, the total applied voltage (V_total) would be divided equally among the coils. For n identical coils in series