Electric Power

When a force causes motion work is done. When one exerts effort to push an object and when such effort causes the object to move forward, work is done. If such an effort did not cause the object to move, such force does not cause work.

Electric power is the rate of doing work. It is the amount of work done by an electrical energy to make the load work. When voltage forces the electrons to move from one point to another, work is done. Electric power is represented by the symbol “P”. The unit used to express electric power is watt (W), named after the Scottish engineer James Watt. The unit watt can be defined as the rate of work done in an electrical circuit in which 1 ampere of current is flowing when 1 volt is applied. In this regard, the power consumed by a resistor can be determined by the voltage drop across it, multiplied by the current flowing through it.

P = IE

where:

• P is the power expressed in watt (W)
• I is the power in ampere (A), and
• E is the voltage expressed in volt (V)

Other formulas derived by combining the power formula and Ohm’s law.

• P = IE
• P = I² R
• P = E² / R

• I = E/R
• I = P/E 
• I = √ P / R 
  

• E = IR
• E = P/I
• E= √ PR

• R = E/I
• R = P / I²
• R = E² / P

Example:

1. In a simple circuit, the power drawn by the load is 500W and the applied voltage is 200 volts. What is the resistance of the load? What is the circuit current?
   
   GIVEN:
   P = 500Watts
   E= 200volts
   R = ?
   I = ?
   
   SOLUTION:
   R = E² / P
   R = (200volts)² / (500watts)
   R = (40 000 v²) / (500watts)
   R = 80 ohms
   
   I = P/E
   I = 500watts / 200volts
   I = 2.5amperes
   
   
2. If the resistor dissipates 1 watt of electrical energy by converting it to heat and the current flowing through it is 2.5A. What is the voltage across the resistor? What is the resistance of the resistor?
   
   GIVEN:
   P = 1 watt
   I = 2.5 amperes
   E= ?
   R = ?
   
   SOLUTION:
   E = P/I
   E = 1 watt / 2.5 ampere
   E = 0.4 volt
   
   R = E/I
   R = 0.4volt / 2.5 ampere
   I = 0.16 ampere

An electrical system or equipment is usually rated in power aside from the voltage rating. An electric soldering iron may have a power rating of 40W or 60W; the wattage rating will tell us the rate at which electrical energy is converted into another form of energy, in the case of soldering iron, it transforms electrical energy into heat. A 60W soldering iron will convert electrical energy to heat energy faster than a 40W soldering iron; the faster the transformation is the greater the heat generated by the soldering iron will be. Same is true with resistors and other electrical equipment and devices. The wattage rating of resistors and other electrical devices indicate the rate at which electrical energy is transformed into heat or some other form of energy. The wattage rating of resistor also indicates the power it can handle without burning itself.