Chapter 29: Alternating Currents

Sinusoidal Current

A sinusoidal alternating current is represented by;

I = I0 sinωt where I0 is the peak value

The current varies like a sine wave so it is called sinusoidal.

Alternating Voltage

The magnitude of the power dissipated in a resistor is given by the expression:

I2R or VI or V2/R

The current and voltage is represented by;

I = I0 sinωt

V = V0 sinωt

And the peak value is I0 and V0.

The power generated in the resistance R is given by the usual Formula

P = I2R

But current I must be written as;

I = I0 sinωt

So,

P = I2R sin2ωt

Since I0 and R are constant so;

= ½ V02/R = ½ I02R

Root mean squared values

Average value of the square of current or voltage is given as;

<I2> = ½ I02

<V2> = ½ V02

SO,

The root mean square value of alternating current is that steady current which delivers the same average power as the a.c. to resistive load.

Transformers

A transformer is a device used to change the voltage of a circuit using electromagnetic induction. It consists of a soft iron core wrapped on both side with wire. The first coil of wire is called primary coil and the other coil is secondary coil.

A current flows through the primary coil which creates magnetic field which cuts through the turns of wire on the secondary coil. This induces the e.m.f. and current in second coil.

Transformers type:

  1. Step Up transformer

Where Vs> Vp or Ns > Np

  1. Step down transformer

Where Vp > Vs or Ns < Np

In both cases

NS/NP = VS/VP = IP/IS

Rectification

It is the process of converting alternating current a.c. into direct current d.c.
Full wave rectification involves four diodes and is referred to as a bridge rectifier circuit. Diodes are used to convert a.c. to d.c. A single diode gives half-wave rectification. A bridge of four diodes gives full-wave rectification. A capacitor soothes the rectified voltage.