Alternating Currents Introduction

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Do we use dry cells for operating electrical appliance? It is not impossible to tap continuous supply of energy from electrochemical cells. Electrical circuits in homes, factories and offices receive such energy form local power companies. In most countries the energy is supplied via oscillating e.m.fs and currents. These oscillating currents are called as alternating currents, shortly as a.c.

Circuits involving alternating currents are used in electric power distribution systems, in radio, TV and other communication devices and in a wide variety of electric motors. The designation 'alternating' mean current changes direction and value periodically with time.

Can you guess the frequency with which their direction is going to alter? In India, the frequency of the alternating current supplied to homes is 50Hz. What does this mean? The current flows along the length of the wire in one direction and changes to the opposite direction, and this happens at the rate of 50 times in one second. That means every 1/100 seconds, there is a change of direction. It is an amazing fact that the charge carriers get this signal of direction change is propagated at the speed of light.

What difference does it make if direct current flows or an alternating current flows in a conductor? As far as the heating effects are concerned such as light bulbs and heaters the direction of current is not important and the electrons transfer the energy to the device via collisions with atoms in the device.

It does make a big difference when the magnetic effects electric current are concerned. As the currents alternate, the magnetic field surrounding the conductor also oscillates. This makes possible the Faraday's laws of induction. Moreover, alternating current is readily adaptable to rotating machinery such as generator and motors.

One of the methods of producing a sinusoid EMF is to rotate the coil in uniform magnetic filed. Graphically, such a varying EMF or current is represented as follows.

Note that E_o and I_o represent the peak or maximum values of EMF at a particular time.

Therefore induced EMF in a coil varies in magnitude and direction periodically. Such an EMF is called alternating EMF. The corresponding current is called alternating current (AC). The AC or EMF first rises to a maximum +E_o or (+I_o) in one direction and falls to zero, the direction then quickly reverses so that the EMF and current rise to maximum value E_o or (-I_o) in the reverse direction and again falls to zero. This completes one cycle of AC voltage, the instantaneous value of EMF is therefore, E = E_o sinwt and current is given by I = I_o sinwt where E_o, I_o are the peak values of the EMF and current and wt are the phase angles.

Average value of alternating e.m.f

Average value of the alternating e.m.f over a half cycle is that steady e.m.f which will send the same amount of charge in a circuit in a time of half cycle as is sent by the given alternating e.m.f in the same circuit in the same time.

Following the above definition, it can be proved that the average value of the alternating value of alternating e.m.f for positive half cycles is 0.637 time the peak value of the alternating current.

Why do we talk about half cycle? What if the whole cycle is taken into account? Due to positive half cycle it is 63.7% _o and then due to negative half cycle it should be -63.7 %_o and hence for the whole cycle the average e.m.f vanishes.

Then how to go about full cycles? We define a new term called 'root mean square value' of e.m.f (or) current.

RMS (Root Mean Square) Value of AC and Alternating EMF

AC can be defined in terms of the heat produced in a resistor due to motion of charges.

The effective value (I_rms or I_eff) of the AC is defined as the value of that direct current which produces the heat at the same rate as the alternating current in a given resistor.

The AC is represented as

I = I_o sinwt

Let the current flow through a resistance R in a small time dt. The amount of heat produced in resistance R is

dH = I² R dt

Total amount of heat produced will be

Now by definition

Similarly,

All electrical elements can be divided into two categories. They are active and passive.

Before analyzing circuit with such alternating EMF or current, it is helpful to discuss the response of each of the three elements (i.e., resistor, inductor, capacitor) separately to such EMF or current. We assume these elements to be ideal. The alternating EMF or current is represented symbolically as