Kirchhoff's Voltage and Current Laws in AC Circuits, Study notes of Law

Download Kirchhoff's Voltage and Current Laws in AC Circuits and more Study notes Law in PDF only on Docsity! 12 Kirchhoff’s Voltage Law (KVL) • The algebraic sum of the voltages around a closed loop (CW/CCW) is zero ( voltage rises =  voltage drops) – Applied to both instantaneous voltages or voltage phasors • Loop 24312 (BCDA, CW): E24+E43+E31+E12=0 or e24+e43+e31+e12=0 • Loop 2342 (ECF, CCW): E23+E34+E42=0 or e23+e34+e42=0 E12 E43 E31 E24 E23 4 2 1 3 E34 E42 13 Kirchhoff’s Current Law (KCL) • The algebraic sum of the currents arriving at a node is equal to 0. ( currents in =  currents out) • Node A: I1+I3=I2+I4+I5 or i1+i3=i2+i4+i5 I1+I3+(-I2)+(-I4)+(-I5)=0 or i1+i3+(-i2)+(-i4)+(-i5)=0 A 16 Impedance angle: >0 for inductive load and <0 for capacitive load         ( ) ( ) ( ) cos( )cos( ) 1 cos( ) cos(2 ) 2 1 cos( ) cos[2( ) ( )] 2 1 cos cos[2( ) ] 2 1 cos cos cos 2( ) sin sin 2( ) 2 m m e i m m e i e i m m e i e e i m m e m m e e p t e t i t E I E I E I E I E I                                                   | | / 2 | | / 2 m m E E I I   e i    ( ) cos [1 cos 2( )] sin sin 2( ) R X e e p p p E I E I                Using trigonometric identity 1 cos cos cos( - ) cos( ) 2 A B A B A B   Instantaneous Power ( ) cos( )m ee t E t   ( ) cos( )m ii t I t   Load Z + t  17 100cose  1.25 60 0.625 1.0825 ΩZ j     80 60 2 I     80cos( 60 )oi   Example: 100 0 2 E    ( ) cos [1 cos 2( )] sin sin 2( ) 2000(1 cos 2 ) 3464 sin 2 R X XR e e p p pp p E I E I                      2000 3464 e i 18 Observations: • The frequency of p, pR and pX is twice of e and i, which is 602=120Hz • pR(t) – changes between 0 and 4000 (=2|E||I|cos ) – always 0, and has an average value of 2000 (=|E||I|cos ) – is the power consumed by the load • pX(t) – changes between 3464 (=  |E||I|sin) – has an average value of 0 – is the power borrowed & returned by the load. ( ) ( ) ( )( ) ( ) cos [1 cos 2( )] sin sin 2( ) (1 cos 2 320 46 n 200 ) 4si R X XR e e p t p t p tp t p t E I E I                    