

Lesson 1: Electric Potential DifferenceElectric Field and the Movement of Charge
Lesson 2: Electric CurrentPower: Putting Charges to Work
Common Misconceptions Regarding
Electric Circuits
Lesson 3: Electrical Resistance
Lesson 4: Circuit ConnectionsCircuit Symbols and Circuit Diagrams 
Lesson 3: Electrical ResistancePower RevisitedThe previous section of Lesson 3 elaborated upon the dependence of current upon the electric potential difference and the resistance. The current in an electrical device is directly proportional to the electric potential difference impressed across the device and inversely proportional to the resistance of the device. If this is the case, then the rate at which that device transforms electrical energy to other forms is also dependent upon the current, the electric potential difference and the resistance. In this section of Lesson 3, we will revisit the concept of power and develop new equations which express power in terms of current, electric potential difference and resistance.
In Lesson 2, the concept of electrical power was introduced. Electrical power was defined as the rate at which electrical energy is supplied to a circuit or consumed by a load. The equation for calculating the power delivered to the circuit or consumed by a load was derived to be (Equation 1) The two quantities which power depends upon are both related to the resistance of the load by Ohm's law. The electric potential difference (V) and the current (I) can be expressed in terms of their dependence upon resistance as shown in the following equations.
If the expressions for electric potential difference and current are substituted into the power equation, two new equations can be derived which relate the power to the current and the resistance and to the electric potential difference and the resistance. These derivations are shown below.
We now have three equations for electrical power, with two derived from the first using the Ohm's law equation. These equations are often used in problems involving the computation of power from known values of electric potential difference (V), current (I), and resistance (R). Equation 2 relates the rate at which an electrical device consumes energy to the current at the device and the resistance of the device. Note the double importance of the current in the equation as denoted by the square of current. Equation 2 can be used to calculate the power provided that the resistance and the current are known. If either one is not known, then it will be necessary to either use one of the other two equations to calculate power or to use the Ohm's law equation to calculate the quantity needed in order to use Equation 2. Equation 3 relates the rate at which an electrical device consumes energy to the voltage drop across the device and to the resistance of the device. Note the double importance of the voltage drop as denoted by the square of V. Equation 3 can be used to calculate the power provided that the resistance and the voltage drop are known. If either one is not known, then it will be important to either use one of the other two equations to calculate power or to use the Ohm's law equation to calculate the quantity needed in order to use Equation 3. While these three equations provide one with convenient formulas for calculating unknown quantities in physics problems, one must be careful to not misuse them by ignoring conceptual principles regarding circuits. To illustrate, suppose that you were asked this question: If a 60watt bulb in a household lamp was replaced with a 120watt bulb, then how many times greater would the current be in that lamp circuit? Using equation 2, one might reason (incorrectly), that the doubling of the power means that the I^{2} quantity must be doubled. Thus, current would have to increase by a factor of 1.41 (the square root of 2). This is an example of incorrect reasoning because it removes the mathematical formula from the context of electric circuits. The fundamental difference between a 60Watt bulb and a 120Watt bulb is not the current that is in the bulb, but rather the resistance of the bulb. It is the resistances which are different for these two bulbs; the difference in current is merely the consequence of this difference in resistance. If the bulbs are in a lamp socket which is plugged into a United States wall outlet, then one can be certain that the electric potential difference is around 120 Volts. The V would be the same for each bulb. The 120Watt bulb has the lower resistance; and using Ohm's law, one would expect it also has the higher current. In fact, the 120Watt bulb would have a current of 1 Amp and a resistance of 120 ; the 60Watt bulb would have a current of 0.5 Amp and a resistance of 240 .
Now using equation 2 properly, one can see why twice the power means that there would be twice the current since the resistance also changes with a bulb change. The calculation of current below yields the same result as shown above.


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