Power in DC Circuits
Whenever a force causes motion, work is performed. Electrical force is expressed as voltage. When voltage causes a movement of electrons (current) from one point to another, energy is expended. The rate of work, or the rate of producing, transforming, or expending energy, is generally expressed in watts or kilowatts. A kilowatt (kW) is 1000 W. In a DC circuit, 1 V forcing a current of 1 A through a 1-W resistance results in 1 W of power being expended. The formula for this is:
P (watts) = E (volts) ´ I (amperes)
Find the power used by the light bulbs in a series circuit. Use the values given in.
I = E RT
I = 10 V
5 W
I = 2 A
Then, because P = E ´ I, P = 10 V ´ 2 A = 20 W. The same calculations can be made for the bulbs in a parallel connection. Total current is 3 A. Applied voltage is 10 V. Since it is a parallel circuit, each resistor will have a 10-V potential across it. Now, use the power formula:
P = E ´ I
P = 10 V ´ 3 A
P = 30 W
Power can be computed if any two of the three values of current, voltage, and resistance are known.
When resistance is unknown:
P = E ´ I When voltage is unknown:
P = I 2 ´ R
When current is unknown:
P E
POWER RATING OF EQUIPMENT
Most electrical equipment is rated for both voltage and power. Electric lamps rated at 120 V are also rated in watts. Then, they are commonly identified by their wattage rating, rather than by voltage. The voltage is usually 120 V in the United States, and 240 V in Europe and certain other countries.
The wattage rating of a light bulb or other electrical device indicates the rate at which electrical energy is changed into other forms of energy, such as light and heat. The greater the amount of electrical power, the brighter the lamp will be. Therefore, a 100-W bulb furnishes more light than a 75-W bulb.
Similarly, the power ratings of motors, resistors, and other electrical devices indicate the rate at which the de- vices are designed to change electrical energy into some other form of energy. If the rated wattage is exceeded, the excess energy is usually converted to heat. Then, the equipment will overheat and this can lead to it being damaged. Some devices will have maximum DC voltage and current ratings instead of wattage. Multiplied, these values give the effective wattage.
Resistors are rated in watts dissipated, in addition to ohms of resistance. Resistors of the same resistance value are available with different wattage ratings. Usually, carbon composition resistors are rated from about
0.1 to 2 W. Carbon composition resistors have color bands to indicate their resistance. The physical size determines their wattage rating. The fourth band deter- mines the tolerance of the resistor.
Wire-wound resistors are used when a higher wattage is needed. Generally the larger the physical size of the resistor, the higher the wattage rating, since a larger amount of surface area exposed to the air is capable of dissipating more heat.