All electrical devices that consume energy must have a resistor (also called a resistance) in their circuit model. Inductors and capacitors may store energy but over time return that energy to the source or to another circuit element. Power in the resistor, given by p ¼ vi ¼ i2 R ¼ v2 =R, is always positive as illustrated in Example 2.1 below. Energy is then determined as the integral of the instantaneous power ð ð t2 ð t2 1 t2 2 2 w¼ p dt ¼ R i dt ¼ v dt R t1 t1 t1 EXAMPLE 2.1. A 4.0- resistor has a current i ¼ 2:5 sin !t (A). Find the voltage, power, and energy over one cycle. ! ¼ 500 rad/s. v ¼ Ri ¼ 10:0 sin !t ðVÞ p ¼ vi ¼ i2 R ¼ 25:0 sin2 !t ðWÞ ðt t sin 2!t ðJÞ w ¼ p dt ¼ 25:0 2 4! 0 The plots of i, p, and w shown in Fig. 2-6 illustrate that p is always positive and that the energy w, although a function of time, is always increasing. This is the energy absorbed by the resistor.
Published on May 10, 2013