Introduction to Electric Circuits

2.3 Circuit elements 29

The coefficient of dI/dt (i.e. tzoN2A/l) is called the coefficient of self-inductance

of the coil or, more usually, simply the inductance of the coil. A coil having

inductance is called an inductor. The symbol for inductance is L and so

L = (tzoN2Z)/l (2.31)

Substituting in Equation (2.30) we have

E = L(dI/dt) (2.32)

From Equation (2.32) we see that the unit of L is the unit of E times the unit of

t divided by the unit of I, i.e. the volt-second per ampere (V s A-l). This is

called the henry in honour of Joseph Henry (1797-1878), an American

mathematician and natural philosopher.

A coil has an inductance of 1 henry when a current changing in it at the rate

of 1 ampere per second causes an emf of 1 volt to be induced in it. The circuit

symbol for inductance is shown in Fig. 2.20.

Figure 2.20

L

o ~ o

Non-linear inductance

If the coil is wound on a ferromagnetic former it is found that the flux density B

is no longer proportional to the magnetic field strength H (i.e. the flux produced

is not proportional to the current producing it). We now write

B =/zH (2.33)

where/z = jt/,r/./,0 and is called the permeability of the medium of the field. It
(and/Zr, the relative permeability) varies widely with B. The inductance is now
given by
L = tXotxrN2A/l (2.34)

This also varies with B (and H and current) and so is non-linear.

Example 2.16

(1) A wooden ring has a mean diameter of 0.2 m and a cross-sectional area of

3 cm 2. Calculate the inductance of a coil of 350 turns wound on it.

(2) If the wooden ring were replaced by one of a ferromagnetic material

having a relative permeability of 1050 at the operating value of magnetic

flux density, determine the new value of inductance.