Lect21 - max max = !" # $% * 07 & + ,- '...

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Unformatted text preview: max max = !" # $% * 07 & + ,- ' (! 0 0 0 0 ) C R * * * * ./ ) . .) . 1 L ! ! ! # !" / ) ! ' ( 3 ) 2 6 ) ) ! ! 8; 1 -! / 4 !)) 789 : 1 1 2 -! ! ) )/ ) ' ) 27 ! ! / ) )5 < I max Vgen Z 0.13 A !" # $% ' (! Vgen = IZ VResistor = I R Vinductor = I XL VCapacitor = I XC & ) C R L 12 # = 1 / ) !)) ! ; < > ) ? ) ! ! @ 1 ! ! ! ' ) ! 8; ) !" 1 ' -! / 2 -! ) )/ ( 3 ) )56 ) ) ! 78779 : 1 ) ! / < / + 1 -! 8 I max Vgen Z 0.13 A 2 1 4 ! ) 27 / ! 9 !" # $% ' (! Vgen = IZ VResistor = I R Vinductor = I XL VCapacitor = I XC & ) C R L 12 # = 1 / ) !)) ! ; < > ) ? ) ! ! @ 1 ! ! ! ' ) ! 8; ) !" 1 ' -! / 2 -! ) )/ ( 3 ) )56 ) ) ! 78779 : 1 ) ! / < / + 1 -! 8 I max Vgen Z 0.13 A 2 1 4 ! ) 27 / ! 2 !" # $% ' (! Vgen = IZ VResistor = I R Vinductor = I XL VCapacitor = I XC & ) C R L 14 # = 1 / ) ! ' !)) ) ! 8; ; )/ ) ? ) !" 1 ' 1 1 ! 7 -! / 2 -! ) )/ ( 3 ) )56 ) ) ! 789 : 1 ) ! / < ) 4 (' < 2 ! ) 4 27 ! 11 ) ! ( 3 ) B 77 77 A7 2 A !) ) C !) ) : 3 ) ) ) ) ' 1 ) ' ' 4 Impedance Z = R at resonance -! ) !( / ! ) ! ) 1 ! ) Resonance in AC Circuits Z XC R Z R 2 (X L XC ) 2 is minimum at resonance XL 0 frequency !) ) B 0 10 5 % (( !) ) Z Q 2 U max U ! " " " D % (( !) ) 7 1! ) Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. Compare the peak voltage across the resistor in the two circuits B. VI = VII C. VI < VII A. VI > VII # % " $ # " # " & 1! ) " Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. Compare the peak voltage across the inductor in the two circuits B. VI = VII C. VI < VII A. VI > VII ' ) " " " " ) ( " ( " ! ) 1! ) Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. Compare the peak voltage across the capacitor in the two circuits B. VI = VII C. VI < VII A. VI > VII * ! " + , , ( ) - " " 1! ) Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. At the resonant frequency, which of the following is true? A. Current leads voltage across the generator B. Current lags voltage across the generator C. Current is in phase with voltage across the generator * , " ! " ) . " / " . ( " 9 Instantaneous power 0 . P(t) varies in time. We want the average power. Average, over one cycle, of any periodic function : P t 1 P t dt T 0 T For harmonically-varying functions like sin t or cos t , Average power: P t 1 V t I t dt T 0 T T 2 2 No average power For L or C. PL ,C t 1 sin T 0 T t cos t dt 0 Average power for R is not zero. PR t I R 2 1 T T I peak sin 0 t 2 Rdt 1 2 I peak R 2 Define root mean square (RMS) I R I RMS 2 1 2 I peak R 2 1 I peak 2 2 I RMS R .707 I peak !' # ( ! ' ) ! ) !) ) 1!' ! ) * * ) 277 ; ) ) < !) 77 .! !!( 2 % 8 6 !' '4 ! ) @ B 0 4. 0 2 1 0 2E 2 E 2 0 0 . !) ) 0 2; F # ( ! ) * * 277 ; !) ) 8 6 !' ) @ B 0 4. 0 8 2 0 . !) ) 0 0 78 2 ; 7 777 .! !1!' ! < 1 ! 01 2 C = ) (! -Time-varying voltage in primary causes time-varying B in iron-core. - flux/ turn = B (Area) = B - Iron core maintains same B throughout. -Primary coil captures flux P = NP B -Secondary coil captures flux S = NS Faraday's Law: VP = d VS = d P S B /dt = NP /dt = NS B B 5 8= 8 3 ) .0. ! / ) ) ! -! / " 92!8 . H + + 4 . . . . . . . . . . . ? @ . . . . . .0. ) . ! G!) . I. ( 07 ) .07 / ) ! -! / D V VL VC VR = 5 ( ) ( " / ) ! -! / " 92! " " " 4 . H ? % . . . . . ) !) ) 7 J! )! / )(! /) . !) ) 0 . . ) ) 7 8= 8 11! ) 0 6 / ) ( ( 3 ! -! ) ) " " " 8 / " 92!8 . H ( " " 4 (A) 0 2 (B) 0 2 2 (C) 0 2 (D) 0 4 XC 2X L 1 C 2 L 2 1 2 LC 1 2 2 0 !) ! ( 3 . 0 77 . 0 27 ) !) 0 - ) 0 !' )8 . H ) ( " ( " " ) (4 Imax 2 mA ? Imax 2 mA 100 50 x103 Imax 2 2 mA !) ) 0 Z R Vmax I max ( 0 ) R 2 mA ...
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