# Andrew Carter

Electrical Engineer

# More of Self Inductance and Mutual Inductance

The principle of action and reaction in Lenz’s Law states that an induced electromotive force (emf) generates a current in a direction which opposes the change in flux that caused the emf in the first place. The basic unit of inductance is called the Henry (H) and a coil has an inductance of 1H when the current flowing through it changes at a rate of one ampere/second inducing a voltage of one volt in it and is given by the equation below:

L = 1H = 1V\frac{dI}{dt} = 1 \frac{volt}{ampere/second}

## Self Inductance

Some inductance may also be present even in a perfectly straight length of conductor because the current can produce a magnetic field surrounding the conductor. Having inductive effects do not really require two circuits. Because all circuits have conductors in them, we can assume that all circuits have inductance. Sometimes, induction can occur when only a single device is present. A changing magnetic field can be created by the changing current through the device.

#### Left Hand Rule

Figure 1 pertains to the left-hand rule which determines the direction of the induced current. The rule states that if you point the thumb of your left hand in the direction of relative motion of the conductor and your index finger in the direction of the magnetic field, the middle finger will now indicate the direction of the induced current which will generate the induced voltage. A coil with many turns will have a higher inductance value than one of only a few turns because the inductance is greater with stronger magnetic flux for a given value of current. The relationship between self inductance (L) and the number of turns (N) is given by the following equation:

L = N\frac{\phi }{I}

This equation applies to linear magnetic materials and can also be defined as the flux linkage divided by the current flowing through each turn.

## Mutual Inductance

The basic operating principle of transformers, motors, generators, and any other electrical component that interacts with another field is the mutual inductance. The relative positioning for the two coils determines the amount of mutual inductance that links one coil to another. The mutual inductance of two circuits depends on several factors such as orientation of circuits, distance between circuits, number of turns in each circuit, size of circuits, and shape of circuits.

#### Mutual Inductance

In Figure 2, the mutual inductance between the two coils can be greatly increased by positioning them on a common soft iron core or by increasing the number of turns of either coil. Unity coupling is said to exist between the two coils due to the leakage of flux if they are tightly wound with one on top of the other over a common soft iron core.

If one coil is positioned next to the other coil so that the physical distance apart from each other is small, then nearly all of the magnetic flux generated by the first coil will interact with the coil turns of the second coil inducing a relatively large emf and therefore producing a large mutual inductance value.

Tags: self inductance, mutual inductance