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
Trnsmsson lne demo
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.
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
E E + + + r + r Now let us put n numers. Suppose: r E E r 0 5 0 " 5 0 + 0 + 0 + + 5 0 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
Exmple wth numers Quk soluton: # E " 4 + 0 6 # 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 + ) " (+ 5 + 5 + + + ) 0 0.65mps 0.65A 6 0
Exmple wth numers (ontnued) Queston: Wht re the termnl voltges of eh ttery? : : 4: $ # r # 0.65A ".75 $ # r # 0.65A ".75 $ # r 4 + 0.65A " 4.65
Multloop Cruts Fnd,, nd We now hve equtons wth unknowns. Krhoff s ules. n ny loop 0 n out. t ny junton 4 7 5 + 4 ( + ) 0 0 4 4 6 0 5 + 6 0 0 multply y multply y sutrt them ule Apply to loops ( nner loops).. ule. 4 0 5 + 4 0 + 9 6 0 9.5A 6 0.5A.0A Fnd the Joule hetng n eh resstor P. s the 5 ttery eng hrged?
Method of determnnts for solvng smultneous equtons 5 4 0 0 4 0 + + Crmer s ule sys f : d d d + + + + + + Then, d d d d d d d d d
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 4 0 5 +4 4 0 " # $ 0 4 0 " # $ 4 4 0 4 % " & ' 0 % " # $ & ' # $ 5 % " & ' 0 % " # $ & ' # $ 0 4 5 4 4 0 4 % & ' % & ' 4 + 48 0 8 + 6 + 5 6 A 0 +4 You try t for nd. See nsde of front over n your ook on how to use Crmer s ule.
Another exmple Fnd ll the urrents nludng dretons. Loop Loop + Loop 0 + 8 + 4 4 0 8 0 8 5 Loop 6 + 4 + 0 Multply eqn of loop y nd sutrt from the eqn of loop 6 + 4 + 0 6 + 6 0 0 0 + 0 A 6 + 4 + (A ) A A 0
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.
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.
When the ul # s not urnt out: eq + Power, P For Bul # For Bul # For Bul # 4 P 9 P 9.44. P 9.
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.66.50 For Bul # P 4.5 So, Bul # gets dmmer nd ul # gets rghter. And the totl power dereses. f) s the nswer.
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?
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
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
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
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
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
Ohmmeter + s + g Adjust s so when 0 the glvnometer red full sle.
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.
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, 000 4 s s g 9, 980 A So, the shunt resstor needs to e out 0KΩ. Note: the voltmeter s n prllel wth the ttery.
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.
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. 7-40 () Wht s the urrent through eh ttery? (Tke upwrd to e postve.) ttery ttery ttery () Wht s the potentl dfferene -?
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 7-47. esstne s djusted so tht when the lp leds re shorted together, the meter deflets to ts full-sle vlue of.00 ma. Fg. 7-47 () 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?