Electric circuit components. Direct Current (DC) circuits

Transcription

1 Electrc crcut components Capactor stores charge and potental energy, measured n Farads (F) Battery generates a constant electrcal potental dfference ( ) across t. Measured n olts (). Resstor ressts flow of charge due to scatterng; dsspates energy. Measured n Ohms (Ω) Drect Current (DC) crcuts Frst, we wll consder crcuts wth batteres and resstors. 5 I R

2 Resstors n Seres The current through all resstors s the same ax xy yb IR IR IR I I I I ( R + R ) ab I R ab IReq Req R + R + R Resstors n Seres R eq R Addng resstors n seres always ncreases the total resstance.

3 Resstors n Seres: Example Calculate I and across each resstor 6 olts I bat R A I A R A.0 Ω R B I B R B.0 Ω Clcker Queston Two dfferent wres are connected to a battery n seres (n a chan, one after another). How does the current n upper wre A compare to the current n lower wre B? A) A > B B) A < B C) A B D) Impossble to determne. I bat R A R B I A I B

4 Resstors n Seres: Example What s the equvalent resstance? R eq R + R.0Ω +.0Ω 4. 0Ω I bat R A I A What s the current through the crcut? Assumng everythng s Ohmc, IR R B I B 6 A B. 5A R 4.0Ω eq Resstors n Seres: Example What about the oltage change across each resstor? 6 olts I bat R A I A R A.0 Ω, A.5 A R B I B R B.0 Ω, B.5 A A A ARA (.5A)(.0Ω). 5 R (.5A)(.0Ω) 4. B B B B 5

5 Clcker Queston If we consder the oltage change startng at Pont P and gong all the way around the crcut loop back to Pont P, what s the total? Α) +6.0 olts Β) +.5 olts C) -4.5 olts D) 0.0 olts E) -6.0 olts Pont P I bat R A R B I A I B Resstors n Seres: Example P I bat R A P P4 I A oltage I R B B P P5 Defne 0 at P Poston In Loop

6 Clcker Queston We start wth the left crcut wth one lghtbulb (A). The brghtness of the bulb drectly reflects the power. If we add a second bulb (B) as shown on the rght, what happens to the bulbs? A)Bulb A s equally brght. B)Bulb A s dmmer than before A A B C)Bulb A s brghter than before Clcker Queston Two lght bulbs, A and B, are n seres, so they carry the same current. Lght bulb A s brghter than B. Whch bulb has hgher resstance? A) A B) B C) Same resstance. Answer: Bulb A has hgher resstance. Snce the resstors are n seres, they have the same current I. Accordng to P I R, f I constant, then hgher R gves hgher P. A B

7 Clcker Queston If we connect a battery wth 6 olts wth three resstors R 0 Ω, R 0 Ω, R 0 Ω, whch of the followng s true? A)The current through each resstor s the same. B)The oltage change through each resstor s the same. C)The resstance of each resstor s the same. D)None of the above are true. Resstors n Parallel The voltage across all resstors s the same I I I / R / R / R I I ab + I + I + R R I + / R eq + Req R R R + R

8 Resstors n Parallel R eq R Addng resstors n parallel always decreases the total resstance. Traffc analog Resstors n parallel are lke havng more lanes on the hghway. Ths reduces the resstance for gettng from one place to another.

9 Resstors n parallel: Example R R I I + + I I R If all three resstors were the same then: I I I I Resstor confguratons Resstors n Seres R eq R + + R R Resstors n Parallel R eq + + R R R Always ncreases the resstance! Always decreases the resstance!

10 Clcker Queston We start wth the left crcut wth one lghtbulb (A). The brghtness of the bulb drectly reflects the power. If we add a second dentcal bulb (B) as shown on the rght, what happens to the bulbs? A B A A)Bulb A s equally brght. B)Bulb A s dmmer than before C)Bulb A s brghter than before Clcker Queston If each of these sx lght bulbs s dentcal, whch bulb s gong to be the brghtest? A)Bulb A B)Bulb B C)Bulb C D)Bulb D E)Bulb E

11 Clcker Queston The three lght bulbs A, B, and C are dentcal. How does the brghtness of bulbs B and C together compare wth the brghtness of bulb A? A) Total power n B+C power n A. A B) Total power n B+C > power n A. C) Total power n B+C < power n A. B C Answer: Use P /R tot For bulbs B and C, R tot R. Total power n B+C < power n A. Clcker Queston In the crcut below, what happens to the brghtness of bulb, when bulb burns out? (When a bulb burns out, ts resstance becomes nfnte.) A) Bulb gets brghter B) Bulb gets dmmer. C) It's brghtness remans the same. (Hnt: What happens to the current from the battery when bulb burns out.)

12 Answers: Bulb gets dmmer! When bulb burns outs, the flament nsde breaks and R becomes nfntely large. The total equvalent resstance whch the battery sees ncreases (snce bulb s gone, there are fewer paths for the current flow, so less flow, more total resstance.) Snce the battery sees a larger R-tot, the current from the battery I-tot /Rtot s reduced. Less current from the battery means less current through bulb, less lght. CPS queston Whch s the best way to wre a house? (A) (B)

13 Resstor networks Resstor networks

14 Krchhoff s rules Krchhoff s oltage Loop Law: The change n oltage around any closed loop must be zero. Krchhoff s Current Juncton Law: In steady state, the current gong nto a juncton (or pont) must equal the current gong out of that juncton (or pont). Clcker Queston What s the electrc potental dfference across the upper lght bulb (resstor)? Thnk about our oltage Loop Rule. A) 0 olts B) 6 olts C) olts D) 4 olts E)None of the above answers.

15 Krchhoff s rules: Example Example : Choose R R R 0 Ω. Longer lne on battery s hgher voltage and the shorter lne s lower voltage, by conventon.. We label the current n each secton as shown. Note that we can guess the b drecton at ths pont. The answer wll be ndependent of our guess. b - + b b Krchhoff s rules: Example. Apply the oltage Loop Rule around each possble loop n the crcut. Make sure to label the drecton of your loop! Make sure to pck a startng pont to go around the loop. Then add up the oltage changes around the loop. b b - b + b

16 Crtcal Sgn Conventon! - + If your loop goes through a battery from to + the oltage ncreases (e.g. + ) - + If your loop goes through a battery from + to the oltage decreases (e.g. - ) Crtcal Sgn Conventon! If you go across a resstor and the loop drecton and guessed current drecton are the same, the voltage decreases (e.g. -R) If you go across a resstor and the loop drecton and guessed current drecton are opposte, the voltage ncreases (e.g. +R)

17 Krchhoff s rules: Example Startng at Pont P go around the loop. bat + R R R sum R + b R R 0 P b - b + b Krchhoff s rules: Example Now try other path startng at Pont P around the new loop. bat + R R R sum R + R R P 0 b - b + b

18 Krchhoff s rules: Example For our specfc crcut, we used R R R 0 Ω sum + R R 0 sum + R R 0 We have two equatons and three unknowns. We need addtonal nformaton Krchhoff s rules: Example Apply the current juncton rule at pont Q below. n out + Also, (as we could have done at the start): b b b Q - + b b

19 Krchhoff s rules: Example Solve equatons and unknowns. 0.8A 0.4 A 0.4A Krchhoff s rules: Example Does ths make sense? snce they are two parallel, equal resstance paths. Current from R and R must go nto R. 0.8A 0.4 A 0.4A - +

20 Clcker Queston What s the value of the equvalent resstor that would replace the three resstors below? A)R eq 5 Ω B)R eq 0 Ω C)R eq 5 Ω D)R eq 0 Ω E)None of the Above R R R 0Ω 0Ω 0Ω 0.8Amps 0.4 Amps 0.4Amps - + Two ways to thnk about t.. Battery of has 0.8 Amps comng out of t. By R the R eq /0.8A5 Ω. R and R are n parallel. R Ω 5 + R R Then R and R are n seres. R eq R R + 5Ω R R 0Ω R 0Ω R 0Ω 0.8Amps 0.4 Amps 0.4Amps - +

21 Clcker Queston Whch of these dagrams represent the same crcut? A. a and b B. a and c C. b and c D. a, b, and c E. a, b, and d Clcker Queston A crcut wth two batteres s shown below. The drectons of the currents have been chosen (guessed) as shown. Whch s the correct current equaton for ths crcut? A)I I + I B) I I + I C) I I + I D) None of these. I R R I Loop. R I

22 Clcker Queston Whch equaton below s the correct equaton for Loop? A) + I R I R 0 B) + I R I R 0 C) I R + I R 0 D) + I R + I R 0 E) None of these. I I Answer: + I R I R 0 R R I Loop. R I Fnsh a full analyss of ths crcut. Consder case:, 4, R R R Ω. R I I R Loop I Loop. R I 0A, 4A, 6A + + R R 4 + R + + R

23 Clcker Queston Two lght bulbs A and B are connected n seres to a constant voltage source. When a wre s connected across B as shown, the brghtness of bulb A... A: ncreases B: decreases, but remans glowng C: decreases to zero (bulb A goes completely dark, no current) D: remans unchanged Answer: Bulb A ncreases n brghtness (snce the current ncreases when B s shorted). Crcut Probes An Ammeter measures the current through tself. An deal Ammeter has zero resstance so t does not affect the crcut! A A To measure the current through R, must place Ammeter n seres. 5 I R

24 Clcker Queston Consder the crcut shown. If you want to measure the current thru bulb, how should the ammeter be attached (assume you only attach one at a tme)? A) Pnk Pnk B) Yellow A A Blue C) Green A 4 Yellow D) Blue A Green E) Two of the 4 postons can be used to measure bulb s current. Answer: B) Yellow Crcut Probes To measure voltage across R, must place oltmeter n parallel wth R. You want the oltmeter to be very hgh resstance (deally nfnty) to avod drawng current. 5 I R

25 Clcker Queston In the crcut shown, what does the voltmeter read? A: 6 B: C: D: 0 E: oltmeter wll "fry" 6 Ω Clcker Queston Now you swtch the voltmeter over to "amp" mode. (But you leave t n the same poston n the crcut) What does the Ammeter read? A: 6 A B: A C: A 6 Ω A D: 0 A E: Ammeter wll "fry" Ammeter wll fry. Ideal Ammeter has zero nternal resstance. If you attach an deal ammeter to a battery, you wll get nfnte power.