Class 12 1 1 W10D2 DC Circuits Today’s Reading Assignment W10D2 DC Circuits & Kirchhoff’s Loop Rules Course Notes: Sections 7.1-7.5 Announcements PS 8 due Week 11 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Next Reading Assignment W10D3 PS07: PhET: Building a Circuit 7.1-7.5, 7.10 Exam 3 Thursday April 24 7:30 pm –9:30 pm Conflict Exam 3 Friday April 25 8-10 am, 10-12 noon If you have a regularly scheduled MIT activity that conflicts with Exam 3, contact [email protected] and explain conflict and request time to take conflict exam. 2 3 Outline DC Circuits Kirchoff’s Laws Electrical Power Measuring Voltage and CurrentClass 12 2 4 DC Circuits 5 Examples of Circuits 6 Symbols for Circuit Elements Battery Resistor Capacitor Switch Equipotential Junction BranchClass 12 3 7 Electromotive Force (EMF) The work per unit charge around a closed path done is called electromotive force EMF. This is a bad name because it is not a force. Let denote the force per unit charge, then the EMF is If a conducting closed path is present then ε= IR fs ε=fs⋅ dsclosd path∫8 Ideal Battery 1) Inside Battery: chemical force , non-zero inside battery (zero outside), moves charges through a region in which static electric field opposes motion 2) Ideal battery: net force on charges is zero 3) Potential difference between its terminals 4) Extend path through external circuit where Estatic= −fs fs Estatic V (+) −V (−) = −Estatic⋅ ds−+∫=fs⋅ ds−+∫ fs=0 V (+) −V (−) =fs⋅ ds−+∫=fs⋅ ds =ε∫9 Kirchhoff’s Loop RulesClass 12 4 10 Charge Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction. I1= I2+ I311 Sum of Potential Differences Around a Closed Path Sum of potential differences across all elements around any closed circuit loop must be zero. ΔVii∑= −Estatic⋅ ds = 0ClosedPath∫12 DC Circuits Rules for Batteries and ResistorsClass 12 5 13 Reference System for Circuit Analysis 1. Simplify resistors in series/parallel. 2. Assign current and current direction in each branch 3. Assign circulation direction for each loop. 4. Circulation direction across each element defines “before” and “after” side of element. 5. Define electric potential difference across a circuit element by ΔV ≡ V (after) − V (before) ≡ V (a) − V (b)14 Sign Conventions - Battery Circulating from the negative to positive terminal of a battery increases your potential ΔV = +ε Circulating from the positive to negative terminal of a battery decreases your potential ΔV = −ε15 Sign Conventions - Resistor Direction of current is the same as direction of electric field which points to lower electric potential Circulating across a resistor in the direction of current decreases the potential Circulating across a resistor in the opposite direction of current increases your potential ΔV = − IR ΔV = + IRClass 12 6 16 Series vs. Parallel Series Parallel 17 Resistors In Series The same current I must flow through both resistors ΔV − I R1+ I R2= 0 ⇒ ΔV = I(R1+ R2) = I Req Req= R1+ R2Circulate Clockwise: 18 Resistors In Parallel Voltage drop across the resistors must be the same ΔV = ΔV1= ΔV2= I1R1= I2R2= IReq I = I1+ I2=ΔVR1+ΔVR2=ΔVReq⇒1Req=1R1+1R2Class 12 7 19 Concept Q: Resistors In Parallel Suppose that . Then the equivalent resistance 1. 2. 3. 4. R1>> R2 Req R2 Req R1 Req R2/ 2 Req R2/ 220 Group Problem: Four Resistors Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is ε, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. Determine the current in each resistor in terms of I. Internal Resistance Real batteries have an internal resistance, r, which is small but non-zero ΔV = Vb− Va=ε− I rTerminal voltage: (Even if you short the leads you don’t get infinite current) Circulate clockwise:Class 12 8 22 Measuring Voltage & Current 23 Measuring Potential Difference A voltmeter must be hooked in parallel across the element you want to measure the potential difference acrossVoltmeters have a very large resistance, so that they don’t affect the circuit too much 1Reffective=1R+1RVoltmeter1R24 Measuring Current An ammeter must be hooked in series with the element you want to measure the current throughAmmeters have a very low resistance, so that they don’t affect the circuit too much Reffective= R + Rammeter RClass 12 9 P18- 25 Concept Question: Measuring Current If R1 > R2, compare the currents measured by the three ammeters: 1. I1 > I2 > I3 2. I2 > I1 > I3 3. I3 > I1 > I2 4. I3 > I2 > I1 5. I3 > I1 = I2 6. None of the above 7. Not enough information is given. 26 Measuring Resistance An ohmmeter must be hooked in parallel across the element you want to measure the resistance ofHere we are measuring R1 Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery) P18- 27 Concept Question: Bulbs & Batteries An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in parallel to the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected 1. is higher. 2. is lower. 3. is the same.Class 12 10 P18- 28 Concept Question: Bulbs & Batteries An ideal battery is hooked to a light bulb with wires. A second identical light bulb is connected in series with the first light bulb. After the second light bulb is connected, the current from the battery compared to when only one bulb was connected 1. is higher. 2. is lower. 3. is the same. 29 Electrical Power Power is change in energy per unit time So power to move current through circuit elements: P =ddtΔU( )=ddtqΔV( )=dqdtΔVVIP Δ=30 Power - Battery I!εIVIP =Δ=suppliedMoving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies powerClass 12 11 31 Power – Resistor (Joule Heating) Moving across a resistor in the direction of current decreases your potential. Resistors always
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