Saturday, October 1, 2011

Power in AC circuits:

Electricity is supplied as an alternating current (A.C.) for domestic and industrial use. The voltage of alternating current is not constant, as in the case of direct current current, (D.C.), and varies sinusoidally with time, at 50 cycles per second (in South Africa).

The alternating potential causes the current in the conductor to change in accordance with Ohm's law. Since the current varies continuously, how is it possible to calculate the heating effect? This can be done by defining effective values of the current, I, and the voltage, V.

"An alternating current is said to have an effective value of 1 ampere when it will develop the same amount of heat in a given resistance as would be produced by a direct current 1 ampere in the same resistance in the same time."

An effective value of the voltage can be defined in an analogous way.

If the effective values of the voltage and current are used, the power dissipation in an A.C. circuit may be calculated in the same way as for direct currents. The effective values are simply the root mean square values of the voltage and current.

In South Africa the effective value of the voltage is quoted as 220V.


Domestic appliances convert electrical energy into other forms of energy. Appliances are generally marked with the recommended operating voltage and their total power consumption at that voltage.

In the case of appliances that produce light and motion, not all the electrical energy is converted into the desired form of energy, as some of the electrical energy is converted to heat. The fraction of energy converted to the desired form is the efficiency of the appliance, e, given by


When a curre nt is passed through a conductor, heat is generated, This is the principle which operates in FUSES. In order to protect equipment or appliances from large, unexpected currents, a fuse (one design is shown on the left) is placed in series in the circuit. It consists of a metal wire designed to melt, and hence break the circuit, o nce the current through it reaches a stated value.

Light bulbs:

An incandescent light bulb consists of an evacuated gla ss container, with conducting supports to hold a coil of fine tungsten wire. As the current passes through the filament, it reaches very high temperatures and emits energy in the form of light. Tungsten is chosen as the metal for the filament as i t has a high melting point (3410 ÂșC). The filament is in a vacuum in order to prevent oxidation of the metal, which would simply burn at the high operating temperature, if air were to be present in the bulb.

Since P = I2R, (the power dissipated in a light bulb is directly proportional to the square of the current flowing through it, and directly proportional to the resistance of the bulb), for a given current flowing through the bulb, the brightness of the light will increase as the resistance increases. On the other hand, for a given applied voltage, the brightness of the light will decrease as the resistance increases. Remember also that
  • A good deal of the power is wasted in generating heat (more than 90%!)
  • The resistance of the bulb will depend on the operating temperature and design of the filament.

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