Magnetic Field Basic Concepts: A current carrying wire produces a magnetic field in the area around it. A time changing magnetic field induces a voltage in a coil (wire) if is passes through the coil (transformer) A moving wire in the presence of a magnetic field has a voltage induced in it (generator) A current-carrying wire in the presence of a magnetic field has a force induced on it (motor).

Faraday’s Law- Induced voltage from a time-varying magnetic field Faraday’s Law for a single wire Faraday’s Law for a coil If we define, : Then we have: Flux linkage

Ideal Transformer

Self and Mutual Inductance In a coil In a transformer

Production of induced force on a wire Direction of l is the same as i

Vector Product

Induced voltage on a conductor moving in a magnetic field Direction of l is such that it would make the smallest angle with The positive side of the resulted voltage in where points

How much do you think the induced voltage is?

AC excitation of magnetic circuits What do we mean by AC excitation? 1- Inserting sinusoid current (what we have considered so far) 2- Applying sinusoid voltage Q: What happens if we somehow insert sinusoid current to a coil? Will the flux and induced voltage be sinusoid as well? A: No, because of saturation and hysteresis Q: What happens if we apply sinusoid voltage to a coil? Will the flux and current (magnetizing current) be sinusoid as well? A: No, because of saturation and hysteresis Conclusion: In a coil current and voltage cannot be sinusoid simultaneously. If one is sinusoid, the other is not.

Let’s see what would happen if we apply sinusoid voltage to a coil?

Magnetization current