Single
phase AC circuits: In dc circuits, voltage applied
& current flowing are constant w.r.t time & to the solution to pure dc
circuits can be analyzed simply by applying ohm`s law.
In ac
circuits, voltage applied & current flowing change from instant to instant.
If a single coil is rotated in a uniform magnetic field, the
currents Ф thus induces are called 1- currents.
A.C.
Through pure Ohmic resistance Alone: The circuit
is shown in Fig Let the applied voltage be given by the equation.
V = Vm
sinwt
Let R = Ohmic resistance; I = instantaneous current.
Obviously, the applied voltage has to supply Ohmic voltage
drop only. Hence for equilibrium
V
= iR;
Putting the value of V from above, we get
Current `i` is maximum when sin
is unity
Im =
Vm/R Hence, equation (ii) becomes, I = Im sinwt
Comparing (i) And (ii), we find that the alternating voltage
and current are in phase with each other as shown in fig. It is also shown
vectorially by vectors VR and I in figure shown below.
Power. Instantaneous
power, P = Vi =
(VmIm/2)-(VmIm/2 Cos2wt)
Power consists of a constant part
and a
fluctuating part
of
frequency double that of voltage and current waves. For a complete cycle the
average of
is zero
Hence, power for the whole cycle is
P =
(VmIm)/2
P = VI Watss
Where V =
rms value of applied voltage .
I = rms value of the current.
It is seen from the fig that no
part of the power cycle becomes negative at any time. In other words, in a
purely resistive circuit, power is never zero. This is so because the
instantaneous values of voltage and current are always either both positive and
negative and hence the product is always positive.]
A.C. Through Pure Inductance Alone:
Whenever an alternating voltage
is applied to a purely inductive coil, a back e.m.f. is produced due to the
self-inductance of the coil. As there is no Ohmic voltage drop, the applied
voltage has to overcome this self – induced e.m.f. Only.
So at every step
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