I.
Self Inductance of a Coil:
The self inductance (L) is given by L =

m0N^{2}A


l

II.
Where m_{0} =

permeability of free space

N =

total number of turns

A =

area of crosssection of coil

l =

length of the coil.

III.
IV.
Mutual Inductance Between Two Coils:
The mutual inductance (M) is given by M = m_{0}

N_{1}N_{2}A


l

V.
Where N, N_{2} = number of turns of the two coils.
VI.
Wattless Current:
If an alternating circuit contains a pure inductor or a pure capacitor only,
its ohmic resistance is zero. The phase difference
between the current and the voltage in such a circuit is 90°. Thus, the power
in the circuit P = E_{rms} × I_{rms} × cos f = E_{rms} I_{rms}
cos 90 = 0.
Hence, there is no dissipation of energy in the circuit. The current in such
a circuit is called wattless current.
VII.
Time Constant:
(a) LR Circuit:
·
When key K is pressed the current in the circuit (shown above)
starts from 0 and increases to a maximum value I_{0}. The growth of
current is given by the equation I = I_{0} (1  e ^{(R/L)t})
Where I_{0} = steady value of current at t = ¥.
The following graph shows the variation of I with t.
·
·
The rate of increase of current becomes less as I approaches I_{0}, it is proportional to R/L.
·
The ratio
is called the time constant and is denoted by l. The time constant l of a circuit is the
time taken by the current to rise from zero to 0.632 or 63.2% of its final
value.
b) C  R circuit:
·
If key K is closed, the charge on the capacitor increases
according to the equation q = CE (1  e^{ }^{t}^{/RC})
= q_{0} (1  e^{
}^{t}^{/RC}).
·
The product RC is called the time constant (l) of the circuit. It
is the time taken by the capacitor to aquire 0.632
or 63.2% of its maximum charge.
