(eosa）=cod=0 sin arcor)sin rcos (12.2.5) 如侧叫号momm(2）-月 (coi m)=oi m=os(2）=月 From the above,we see that the average of the square of the current is non-vanishing: o)=0通=%smah=sm(2）血=22 It is convenient to define the root-mean-square(rms)current as -芳 (12.2.7) In a similar manner,the rms voltage can be defined as -o-芳 (12.2.8) The rms voltage supplied to the domestic wall outlets in the United States is V'ms=120 Vat a frequencyf=60 Hz. The power dissipated in the resistor is PR(t)=Ig(t)VR(t)=IR(t)R (12.2.9) from which the average over one period is obtained as: o-2@R=5aR=R=1-g (12.2.10) R 12.2.2 Purely Inductive Load Consider now a purely inductive circuit with an inductor connected to an AC generator, as shown in Figure 12.2.3. 12-50 0 2 2 2 0 0 2 2 2 0 0 1 cos cos 0 1 sin cos sin cos 0 1 1 2 sin sin sin 2 1 1 2 cos cos cos 2 T T T T T T t t dt T t t t t dt T t t t dt dt T T T t t t dt dt T T T ω ω ω ω ω ω π ω ω π ω ω = = = = ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ ∫ ∫ ∫ ∫ ∫ ∫ 1 1 = = (12.2.5) From the above, we see that the average of the square of the current is non-vanishing: 2 2 2 2 2 2 0 0 0 0 0 1 1 1 2 ( ) ( ) sin sin 2 T T T R R R R t 2 0 1 R I t I t dt I t dt I dt I T T T T π ω ⎛ ⎞ = = = ⎜ ⎟ = ⎝ ⎠ ∫ ∫ ∫ (12.2.6) It is convenient to define the root-mean-square (rms) current as 2 0 rms ( ) 2 R R I I I = t = (12.2.7) In a similar manner, the rms voltage can be defined as 2 0 rms ( ) 2 R R V V V = t = (12.2.8) The rms voltage supplied to the domestic wall outlets in the United States is at a frequency . rms V =120 V f = 60 Hz The power dissipated in the resistor is (12.2.9) 2 ( ) ( ) ( ) ( ) P t R R R R = I t V t = I t R from which the average over one period is obtained as: 2 2 2 2 rms 0 rms rms rms 1 ( ) ( ) 2 R R R V P t I t R I R I R I V R = = = = = (12.2.10) 12.2.2 Purely Inductive Load Consider now a purely inductive circuit with an inductor connected to an AC generator, as shown in Figure 12.2.3. 12-5