PHY2049: Chapter 271CircuitsPHY2049: Chapter 272What You Already KnowÎNature of currentÎCurrent densityÎDrift speed and currentÎOhm’s lawÎConductivity and resistivityÎCalculating resistance from resistivityÎPower in electric circuitsPHY2049: Chapter 273Chapter 27: Electric Circuits ÎWork, energy and EMFÎSingle loop circuitsÎMultiloop circuitsÎAmmeters and voltmetersÎRC circuits and time constantPHY2049: Chapter 274Reading Quiz for Chapter 27ÎThe electric current is defined as: (1) amount of charge per time (2) amount of charge per area (3) amount of charge per volumeÎWhen resistors are connected in series (1) the current in each resistor is different (2) the current in each resistor is the same (3) the voltage in each resistor is the sameÎWhich of the following is not related to Kirchhoff’s Rules? (1) conservation of charge (2) conservation of energy (3) conservation of momentumPHY2049: Chapter 275EMFÎEMF device performs work on charge carriers Converts energy to electrical energy Moves carriers from low potential to high potential Maintains potential across terminalsÎVarious types of EMF devices Battery Electrolytic reaction Generator Magnetic field Fuel cell Oxidation of fuel Solar cell Electromagnetic energy Thermopile Nuclear decayÎExample: battery Two electrodes (different metals) Immersed in electrolyte (dilute acid) One electrode develops + charge, the other – chargePHY2049: Chapter 276Common dry cell batteryPHY2049: Chapter 277Electrons in the wireÎIf the electrons move so slowly through the wire, why does the light go on right away when we flip a switch? Household wires have almost no resistance The electric field inside the wire travels much faster Light switches do not involve currents None of the abovePHY2049: Chapter 278Electrons in the wire, part 2 ÎOkay, so the electric field in a wire travels quickly. But, didn’t we just learn that E = 0 inside a conductor? True, it can’t be the electric field after all!! The electric field travels along the outside of the conductor E = 0 inside the conductor applies only to static charges None of the abovePHY2049: Chapter 279Series CircuitÎSimple series situation 1 battery and two resistors R1and R2 Common current IÎTotal voltage E = V1+ V2E = IR1+ IR2≡ IRs Rs= R1+ R2ÎSo equivalent resistance is the sum Works for any number of resistors Rs= R1+ R2+ R3+ R4+ …PHY2049: Chapter 2710Resistors in seriesÎEMF of battery is 12 V, 3 identical resistors. What is the potential difference across each resistor? 12 V 0 V 3 V 4 VCurrent is the same, so voltageacross each is the same RRRPHY2049: Chapter 2711Resistors in seriesÎIf the light bulbs are all the same in each of these two circuits, which circuit has the higher current? circuit A circuit B both the sameÎIn which case is each light bulb brighter? circuit A circuit B both the sameABPHY2049: Chapter 2712Real EMF Sources: Internal ResistanceÎReal batteries have small internal resistance Lowers effective potential delivered to circuitC CaVbVrREirR=+eff baVVVEirEErrR=−=−=−+eff1/EVrR=+This is the voltage measured across the terminals!PHY2049: Chapter 2713Internal Resistance ExampleÎLoss of voltage is highly dependent on loadÎE= 12V, r= 0.1Ω, R= 100Ω Loss of 0.01VÎE= 12V, r= 0.1Ω, R= 10Ω Loss of 0.1VÎE= 12V, r= 0.1Ω, R= 1Ω Loss of 1.1VÎE= 12V, r= 0.1Ω, R= 0.5Ω Loss of 2.0Veff12/1.01 11.9VV==eff12/1.1 10.9VV==eff12/1.2 10.01VV==eff12/1.001 11.99VV==eff121/ 10.1/EVrR R==++PHY2049: Chapter 2714Heating From Internal ResistanceÎHeating of EMF source: P = i2r Heating is extremelydependent on loadÎE= 12V, r = 0.1Ω R = 100Ω Vba= 11.99V I = 0.12 A P = 0.0014 W R = 10Ω Vba= 11.9V I = 1.19 A P = 0.14 W R = 1.0Ω Vba= 10.9V I = 10.9 A P = 11.9 W R = 0.5Ω Vba= 10.0V I = 20 A P = 40 W()22214.40.1EPir rrRR⎛⎞== =⎜⎟+⎝⎠+PHY2049: Chapter 2715Resistors in ParallelÎ Current splits into several branches. Total current is conserved I = I1+ I2Î Potential difference is same across each resistor V = V1= V2adIR1R2I1I2V12pVVVRRR=+12111pRRR=+IadIIVIRpRp= equivalent resistance. Works forany number of resistorsPHY2049: Chapter 2716ÎAs more resistors R are added in parallel to the circuit, how does total resistance between points P and Q change? (a) increases (b) remains the same (c) decreasesÎIf the voltage between P & Q isheld constant, and more resistorsare added, what happens tothe current through each resistor? (a) increases (b) remains the same (c) decreasesResistors in ParallelOverall current increases,but current through eachbranch is still V/R.PHY2049: Chapter 2717Resistance Example ÎFind net resistance of the circuit connected to the battery. Each resistance has R = 3 kΩPHY2049: Chapter 2718Resistance Example (1+2) ÎCombine #1 & #2 in series R12= 6 kΩPHY2049: Chapter 2719Resistance Example (1+2+3)ÎCombine 6kΩ & #3 in parallel R123= 2 kΩPHY2049: Chapter 2720Resistance Example (1+2+3+4)ÎCombine 2kΩ & #4 in series R1234= 5 kΩABCACPHY2049: Chapter 2721ACResistance Example (1+2+3+4+5)ÎCombine 5kΩ & #5 in parallel R12345= 1.875 kΩACPHY2049: Chapter 2722Resistance Example (1+2+3+4+5+6)ÎCombine 1.875kΩ & #6 in series R123456= 4.875 kΩACPHY2049: Chapter 2723CircuitsÎIf the light bulbs are all the same in each of these two circuits, which circuit has the higher current? (a) circuit A (b) circuit B (c) both the sameÎIn which case is each light bulbbrighter? (a) circuit A (b) circuit B (c) both the sameABCurrent through eachbranch is unchanged (V/R)B draws twice the current as APHY2049: Chapter 2724Light Bulb ProblemÎTwo light bulbs operate at 120 V, one with a power rating of 25W and the other with a power rating of 100W. Which one has the greater resistance? (a) the one with 25 W (b) the one with 100 W (c) both have the same resistanceÎWhich carries the greater current? (a) the one with 25 W (b) the one with 100 W (c) both have the same currentP = I2R = V2/R, so 100W bulb has¼ the resistance of the 25W bulband carries 4x the current.PHY2049: Chapter 2725Dimmer ÎWhen you rotate the knob of a light dimmer, what is being changed in the electric circuit? (a) the voltage (b) the resistance (c) the current (d) both (a) and (b) (e) both (b) and
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