LECTURE 8
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Name Name(please (please print) print) Physics 132 Quiz # 14 1.1. Which Whichis(are) is(are)true? true?Kirchhoff’s Kirchhoff’ssecond secondrule rulerelates relates a.) a.) the thesum sumof ofthe theemfs emfsaround aroundaaclosed closedloop loopininaa circuit circuittotothe thepotential potentialchanges changesacross acrossall allresistors resistors and andcircuit circuitelements. elements. b.) b.) implies impliesconservation conservationof ofenergy energyininelectric electric circuits. circuits. c.) c.) relates relatesthe thecurrents currentsentering enteringand andleaving leavingany any branch branchpoint pointininaacircuit. circuit. d.) d.) all allof ofthe theabove above e.) e.) two twoof ofthe theabove above f.) f.) none noneof ofthe theabove above 2.2. AAresistor resistorand andan aninitially initiallyuncharged unchargedcapacitor capacitor arranged arrangedininseries seriesare arecharged chargedby byaabattery, battery,which which isisconnected connectedatattt==0.The 0.Thecurrent currentininthe thecircuit circuit a.) a.) isisconstant constantbecause becausethe theemf emfsupplied suppliedby bythe the battery batteryisisconstant. constant. b.) b.)decreases decreasesexponentially exponentiallyinintime. time. c.) c.)increases increasesexponentially exponentiallyinintime. time. d.) d.)There Thereisisno nocurrent currentbecause becausethe theelectrons electrons cannot cannotflow flowthrough throughthe thegap gapininthe thecapacitor. capacitor. LECTURE 15 •• •• •• •• Announcement Announcement Office Office Hours Hours (today (today ONLY) ONLY) 2:00-3:00 2:00-3:00 pm pm in in 284 284 NSH NSH 3:00-4:00 3:00-4:00 pm pm in in 235 235 NSH NSH HW HW questions questions during during office office hours: hours: must must show show work work on on the the problem, problem, and and must must have have specific specific question question Wednesday Wednesday lecture: lecture: more more practice practice of of DC DC circuits circuits New New assignment assignment handed handed out out on on Wednesday Wednesday Kirchhoff’s rules for electric circuits Typical Typicalproblem problem Given: Given: ••resistors, resistors, ••batteries, batteries, ••connections connections Find: Find: •current •currentthrough, through, •voltage •voltageacross across any anycircuit circuitelement element Gustav Robert Kirchhoff I.I. Rule Rulefor for“nodes” “nodes” “current “currentin=current in=currentout” out” Example: I1 J1 I2 I3 J2 I1 + I 2 + I 3 = J 1 + J 2 I= ∆Q ∆t ⇓ ∆Q1 ∆Q2 ∆Q3 ∆q1 ∆q2 =0 − − + + ∆t ∆t ∆t ∆t ∆t c ∆Q1 + ∆Q2 + ∆Q3 − ∆q1 − ∆q2 = 0 Charge on the node is conserved II. II.Rule Rulefor for“loops” “loops” “Algebraic “Algebraicsum sumof ofpotential potentialchanges changes==zero” zero” E1 E2 Energy Energyisis conserved conserved II. II.Rule Rulefor for“loops”(cont’d) “loops”(cont’d) “Algebraic “Algebraicsum sumof ofpotential potentialchanges changes==zero” zero” − IR1 − IR2 − E2 − Ir2 − IR3 + E1 − Ir1 = 0 E1 − E2 I= R1 + R2 + R3 + r1 + r2 Alternate form: E1 − E2 = IR1 + IR2 + Ir2 +IR3 + Ir1 “Loop rule”: Sum of E’s = sum of IR’s Basic strategy: WATCH FOR +/- SIGNS!! 1. Label each battery with + (long side) and – (short side) 2. Label the current in each branch with a symbol and an arrow (arbitrary direction). 3. Apply Kirchhoff’s node rule to one node 4. Apply Kirchhoff’s loop rule to a loop: a. Choose a direction (clockwise or counter-clockwise) to “go” around a loop b. Battery E is positive, if your direction of circulation takes you from the “-” pole to the “+” pole of the battery c. Product IR is positive if direction of circulation coincides with current direction on the resistor d. Write “Sum of E’s = Sum of IR’s” 5. Repeat 3-4 until # eqs. = # unknowns 6. Solve for unknowns (currents, for e.g.) Problem 1: Calculate the current in the circuit R2= 15 kΩ R1= 5 kΩ I + - E=12 V CONCEPT TEST: TEST: CONCEPT Twoidentical identicallight lightbulbs bulbs AAand andBBare are wired wiredin in Two seriesand andconnected connectedto toaapower powersupply, supply,as asshown shown series inthe thefigure. figure.When Whenthe theswitch switchisisclosed, closed,the the in brightnessof ofbulb bulbAA brightness 1.increases increases 1. remainsthe thesame same 2.2.remains 3.decreases decreases 3. A B Problem 2: Calculate the current in each branch of the circuit below: R1= 5 kΩ I1 I2 I R2= 5 kΩ + E=12 V R3= 15 kΩ CONCEPT TEST: TEST: CONCEPT Thelight lightbulbs bulbs in inthe thecircuit circuitare areidentical. identical.When When The theswitch switchisisclosed closed the bothgo goout out 1.1.both 2.AAbecomes becomesbrighter brighter 2. 3.BBbecomes becomesbrighter brighter 3. 4.AAbecomes becomesdimmer dimmer 4. becomesdimmer dimmer 5.5.BBbecomes combinationof of1-5 1-5 6.6.combination nothingchanges changes 7.7.nothing 12 V 12 V 12 V Example: Wheatstone bridge: measures resistance a.) Draw the equivalent circuit when the bridge is balanced, and write Kirchoff’s laws b.) calculate Rx if the bridge is balanced at 18 cm
