**Relation
between RMS value and peak value (I _{v} and I_{o})**

Consider an AC through a circuit of resistance R. Let
the current at any instant be I = I_{o
}sin ∞t. By Joules law heat
produced per second = I^{2}Rt = I^{2}_{0 }sin^{2} ∞t x R x 1 (Here t = 1)

Consider two circuits kept close to each other as in
fig.2. The magnetic flux produced in one
circuit will affect the other also.
Changes of current in one circuit will produce changes of flux in that
circuit and this will change the flux through other circuit. Therefore an emf will be induced in secondary
circuit due to current changes in the other circuit. This is the principle of mutual induction. The phenomenon by which an emf is induced in
a circuit due to the change of current in a neighbouring circuit is called
mutual induction. If one coil is wound
over the other the effect of mutual induction is greater.

The induced emf in a circuit is proportional to the
rate of change of flux in that circuit and this will be proportional to the
rate of change of current in the other circuit.
Thus the induced emf in the secondary is proportional to dI/dt, the rate
of change of current in the primary.

Therefore the mutually induced emf = a constant x
(dI/dt). This constant is called the
coefficient of mutual inductance or mutual inductance between the two circuits
and it is represented by M.

∴ Mutually induced emf =

The negative sign indicated that the induced emf opposes the change of
flux. If (dI/dt) = 1, then mutually induced emf = M (numerically)