Lecture 7 Circuits Ch. 27

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3 Leture 7 Cruts Ch. 7 Crtoon -Krhhoff's Lws Tops Dret Current Cruts Krhhoff's Two ules Anlyss of Cruts Exmples Ammeter nd voltmeter C ruts Demos Three uls n rut Power loss n trnsmsson lnes esstvty of penl Blowng fuse Elmo

4 Trnsmsson lne demo

5 Krhhoff's Lws. The sum of the potentl drops round losed loop s zero. Ths follows from energy onservton nd the ft tht the eletr feld s onservtve fore.. The sum of urrents nto ny junton of losed rut must equl the sum of urrents out of the junton. Ths follows from hrge onservton.

6 No junton so we don t need tht rule. How do we pply Krhhoff s rule? Exmple (Sngle Loop Crut) Must ssume the dreton of the urrent ssume lokwse. Choose strtng pont nd pply Ohm s Lw s you go round the rut.. Potentl ross resstors s negtve. Sgn of E for ttery depends on ssumed urrent flow. f you guessed wrong on the sgn, your nswer wll e negtve Strt n the upper left hnd orner. E r + E r 0 E E r + r

7 E E r + r Now let us put n numers. Suppose: r E E r " mp Note tht we ould hve smply dded ll resstors nd get the eq. nd dded the EMFs to get the E eq. And smply dvded. E eq. e q. 5( ) ( ) Sgn of EMF 5 mp Suppose: E E 5 0 ( 5 0) 5 mp " We get mnus sgn. t mens our ssumed dreton of urrent must e reversed. Bttery urrent flows from - to + n ttery +E Bttery urrent flows from + to - n ttery -E n the eletrl potentl energy nreses n the eletrl potentl energy dereses

8 Exmple wth numers Quk soluton: # E " # E 6 eq. e q. 0 6 A Queston: Wht s the urrent n the rut? Wrte down Krhhoff s loop equton. Loop equton Assume urrent flow s lokwse. Do the tteres frst Then the urrent. ( + " 4 + ) " ( ) mps 0.65A 6 0

9 Exmple wth numers (ontnued) Queston: Wht re the termnl voltges of eh ttery? : : 4: $ # r # 0.65A ".75 $ # r # 0.65A ".75 $ # r A " 4.65

10 Multloop Cruts Fnd,, nd We now hve equtons wth unknowns. Krhoff s ules. n ny loop 0 n out. t ny junton ( + ) multply y multply y sutrt them ule Apply to loops ( nner loops).. ule A 6 0.5A.0A Fnd the Joule hetng n eh resstor P. s the 5 ttery eng hrged?

11 Method of determnnts for solvng smultneous equtons Crmer s ule sys f : d d d Then, d d d d d d d d d

12 Method of determnnts usng Crmers ule nd oftors Also use ths to rememer how to evlute ross produts of two vetors. For exmple solve for " # $ " # $ % " & ' 0 % " # $ & ' # $ 5 % " & ' 0 % " # $ & ' # $ % & ' % & ' A 0 +4 You try t for nd. See nsde of front over n your ook on how to use Crmer s ule.

13 Another exmple Fnd ll the urrents nludng dretons. Loop Loop + Loop Loop Multply eqn of loop y nd sutrt from the eqn of loop A (A ) A A 0

14 ules for solvng multloop ruts. eple seres resstors or tteres wth ther equvlent vlues.. Choose dreton for n eh loop nd lel dgrm.. Wrte the junton rule equton for eh junton. 4. Apply the loop rule n tmes for n nteror loops. 5. Solve the equtons for the unknowns. Use Crmer s ule f neessry. 6. Chek your results y evlutng potentl dfferenes.

15 ul queston The rut ove shows three dentl lght uls tthed to n del ttery. f the ul# urns out, whh of the followng wll our? ) Buls nd re unffeted. The totl lght emtted y the rut dereses. ) Buls nd get rghter. The totl lght emtted y the rut s unhnged. ) Buls nd get dmmer. The totl lght emtted y the rut dereses. d) Bul gets dmmer, ut ul gets rghter. The totl lght emtted y the rut s unhnged. e) Bul gets rghter, ut ul gets dmmer. The totl lght emtted y the rut s unhnged. f) Bul gets dmmer, ut ul gets rghter. The totl lght emtted y the rut dereses. g) Bul gets rghter, ut ul gets dmmer. The totl lght emtted y the rut dereses. h) Bul s unffeted, ut ul gets rghter. The totl lght emtted y the rut nreses. ) None of the ove.

16 When the ul # s not urnt out: eq + Power, P For Bul # For Bul # For Bul # 4 P 9 P P 9.

17 When the ul # s urnt out: eq + Power, P For Bul # For Bul # P 4 0 P 0.5 Before totl power ws After totl power s P P eq eq For Bul # P 4.5 So, Bul # gets dmmer nd ul # gets rghter. And the totl power dereses. f) s the nswer.

18 How does ptor ehve n rut wth resstor? Chrge ptor wth 9 ttery wth swth open, then remove ttery. Now lose the swth. Wht hppens?

19 Dshrgng ptor through resstor Potentl ross ptor C just efore you throw swth t tme t 0. Potentl ross esstor Q C o o o Qo C Qo t t > 0. (t) Wht s the urrent t tme t? or (t) Q(t) C Q C

20 Wht s the hrge Q t tme t? Q So,, ut C dq dt dq Q Q C dt C dq dt Tme onstnt C So, ntegrtng oth the sdes dq dt " Q C t ln Q + A C t ln Q A C Q e t A C e t C e A Q Q 0 t C Q e Q.7 t At t0, QQ 0 So, Q 0 A C A 0 e e " Q Q 0 e t C

21 Wht s the urrent? t Q Q e C 0 dq dt C Q t 0 C 0 e e t C gnore - sgn 0 C t

22 How the hrge on ptor vres wth tme s t s eng hrged Wht out hrgng the ptor? C 0 Q 0 Q Q C 0 ( e t C ) t 0 e t " Sme s efore Note tht the urrent s zero when ether the ptor s fully hrged or unhrged. But the seond you strt to hrge t or dshrge t, the urrent s mxmum. t

23 nstruments Glvnometers: Ammeters: oltmeter: Ohmmeters: Multmeters: ol n mgnet feld tht senses urrent. mesures urrent. mesures voltge. mesures resstne. one deve tht does ll the ove. Glvnometer s needle mounted to ol tht rottes n mgnet feld. The mount of rotton s proportonl to the urrent tht flows through the ol. Symollly we wrte g Usully when g 0 g 0 0.5mllAmp

24 Ohmmeter + s + g Adjust s so when 0 the glvnometer red full sle.

25 Ammeter g 0 5A g 5A s 5A The de s to fnd the vlue of S tht wll gve full sle redng n the glvnometer for 5A s g + s 5A g g s s g 0$ nd g 0.5 # 0 " A, So, s 5A ".0005A 5A So, s g s g 0.5 " 0 5A # A (0) 0.00 ery smll Ammeters hve very low resstne when put n seres n rut. You need very stle shunt resstor.

26 oltmeter Use the sme glvnometer to onstrut voltmeter for whh full sle redng n 0 olts. 0 s g g 0.5 " 0 g # 0 A Wht s the vlue of S now? We need 0 g (s + g) 0 0 s + g g 5 " 0 + 0, s s g 9, 980 A So, the shunt resstor needs to e out 0KΩ. Note: the voltmeter s n prllel wth the ttery.

27 Chpter 7 Prolem 9 n Fgure 7-4, 00, 0, nd the del tteres hve emfs srpt e 6.0, srpt e 5.0, srpt e.0. Fg. 7-4 () Fnd the urrent n resstor. Fg. 7-4 () Fnd the urrent n resstor. () Fnd the potentl dfferene etween ponts nd.

28 Chpter 7 Prolem 7 n Fgure 7-40, the resstnes re 0.5,.7, nd the del tteres hve emfs srpt e.0, nd srpt e srpt e. Fg () Wht s the urrent through eh ttery? (Tke upwrd to e postve.) ttery ttery ttery () Wht s the potentl dfferene -?

29 Chpter 7 Prolem 8 A smple ohmmeter s mde y onnetng 4.0 ttery n seres wth resstne nd n mmeter tht reds from 0 to.00 ma, s shown n Fgure esstne s djusted so tht when the lp leds re shorted together, the meter deflets to ts full-sle vlue of.00 ma. Fg () Wht externl resstne ross the leds results n defleton of 0% of full sle? () Wht resstne results n defleton of 50% of full sle? () Wht resstne results n defleton of 90% of full sle? (d) f the mmeter hs resstne of 40.0 nd the nternl resstne of the ttery s neglgle, wht s the vlue of?

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