Again,Kirchhoff's voltage rule implies )-Ve(0=r0-0=0 (12.2.18) which yields Q(t)=CV(t)=CVc(t)=CVco sin@t (12.2.19) where Vco=.On the other hand,the current is (12.2.20) d where we have used the trigonometric identity cosot sin 0t+ (12.2.21) 2 The above equation indicates that the maximum value of the current is Ico =@CVco=- (12.2.22) Xc where 1 Xc=- (12.2.23) OC is called the capacitance reactance.It also has SI units of ohms and represents the effective resistance for a purely capacitive circuit.Note that X is inversely proportional to both C andand diverges as approaches zero. By comparing Eq.(12.2.21)to Eq.(12.1.2),the phase constant is given by (12.2.24) 2 The current and voltage plots and the corresponding phasor diagram are shown in the Figure 12.2.6 below. 12-8Again, Kirchhoff’s voltage rule implies ( ) ( ) ( ) ( ) 0 C Q t V t V t V t C − = − = (12.2.18) which yields 0 ( ) ( ) ( ) sin Q C C t = = CV t CV t =CV ωt (12.2.19) where . On the other hand, the current is VC0 =V0 0 0 ( ) cos sin 2 C C C dQ I t CV t CV t dt π ω ω ω ω ⎛ = + = = ⎜ + ⎝ ⎠ ⎞ ⎟ (12.2.20) where we have used the trigonometric identity cos sin 2 t t π ω ω ⎛ = ⎜ + ⎝ ⎠ ⎞ ⎟ (12.2.21) The above equation indicates that the maximum value of the current is 0 0 0 C C C C V I CV X =ω = (12.2.22) where 1 XC ωC = (12.2.23) is called the capacitance reactance. It also has SI units of ohms and represents the effective resistance for a purely capacitive circuit. Note that XC is inversely proportional to both C and ω , and diverges as ω approaches zero. By comparing Eq. (12.2.21) to Eq. (12.1.2), the phase constant is given by 2 π φ = − (12.2.24) The current and voltage plots and the corresponding phasor diagram are shown in the Figure 12.2.6 below. 12-8