Is the Induced EMF additive to the circuit

emfseries

From the following diagram:
enter image description here

Assume that +V(S), is a applied voltage from a power supply, and current I is flowing now in the circuit, and I introduced a (negatively)changing magnetic flied covering a small volume of that conductor, and an EMF is induced in such a polarity above. The circuit as a whole is like so:

schematic

simulate this circuit – Schematic created using CircuitLab

Where (D) is the diagram above the circuit schematic, is total applied voltage on the load equal to the induced EMF added to the applied voltage +V? $$V_t = V_S + V_E$$

Because the induced EMF is now in series with the applied voltage?
I guess, my confusion with this is the magnetic field is covering a small area, would the voltage still be additive? Vs. the magnetic field covering a larger area inducing a larger EMF at the same polarity?

Best Answer

Your top diagram doesn't make much sense. However, if you have a closed loop of a power supply and resistor as you show, then the EMF induced by a changing magnetic field enclosed by the loop will add or subract from the power supply voltage, depending on the polarity of the magnetic field change.

You can actually wire this up and see it. Make a circuit of a power, supply, resistor, and the secondary of a transformer, all in series. Assuming the transformer secondary DC resistance is small compared to the resistor, it's effectively not there as long as the primary of the transformer is not driven. When the primary is driven, there will be a corresponding AC voltage induced across the secondary. This secondary is in series with the supply, so the resistor will "see" this voltage plus the supply's voltage at any instance. Note that overall, the transformer will only put out AC, so at times it will add to the supply and at other times subtract from it.

For example, let's say you have a 7 V supply in series with a transformer secondary that puts out 1 V peak AC sine. The resistor will see the voltage varying sinusoidally between 6 V and 8 V.