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Transcript
LECTURE 12 KIRCHHOFF’S RULES & MULTILOOP CIRCUITS Lecture 12 2 ¨ Reading chapter 25-4 and 25-5. ¤ Combination of resistors n Series n Parallel ¤ Kirchhoff’s rules ¤ Ammeters, voltmeters, and ohmmeters Quiz: 1 3 Resistors in series 4 ¨ ¨ ¨ The current through each resistor must be the same. The potential drop across a single equivalent resistor must equal the sum of the potential drops across the individual resistors. In general, for n resistors in series, the equivalent resistance is Quiz: 2 5 Resistors in parallel 6 ¨ ¨ ¨ The potential drop across each resistor is the same as that across a single equivalent resistor. The total current is equal to the sum of the current through each resistor. In general, for n resistors in parallel, the equivalent resistance can be calculated with Demo: 1 7 ¨ Series and parallel light bulbs ¤ Demonstration of the different current in the two circuits, three light bulbs in series and in parallel, by the relative brightness of the bulbs. Example: 1 8 ¨ Find R3 so that the equivalent resistance between terminals a and b, Rab, is equal to R1. Demo: 2 9 ¨ Conservation of current ¤ Demonstration of the current flowing into a junction equaling the current flowing out the junction. I2 I1 = I2 + I3 I1 I3 Kirchhoff’s rules 10 ¨ Junction rule: the sum of the currents into a junction must equal the sum of the currents out of the junction. ¤ ¨ 𝐼" = 𝐼$ + 𝐼& Loop rule: The sum of the changes in potential around any closed loop must equal zero. ¤ ¤ ¤ ¤ ∆𝑉)* + ∆𝑉+, = 0 The potential drops passing through a resistor in the direction of the current. The potential increase going from the negative terminal to positive terminal of a battery. +ℇ − 𝐼𝑅 = 0 Quiz: 3 & 4 11 What is the current through R? 12 V V V V V V V Good loop 13 V V V V V V V +V + V + V − V − IR = 0 → I = 2V R Example: 2 14 ¨ Assume that R1 = 1.0 Ω, R2 = 2.0 Ω, E1 = 2.0 V, and E = E2 = E3 = 4.0 V. a) b) Calculate the current through each ideal battery. Calculate Va - Vb. Quiz: 5 15 Galvanometers 16 ¨ ¨ A galvanometer is a device that detects small currents passing through it. The scale reading is proportional to the current passing through. Ammeters 17 ¨ ¨ An ammeter is a device that measures currents passing through it. To measure the current in the resistor, ammeter has to be connected in series. ¨ Ammeters have very small resistance to minimize the effect of itself on the current through the circuit. We can construct an ammeter by connecting a galvanometer in parallel with a shunt resistor, which has a small resistance Rp. The majority of the current passes through Rp. ¨ The current flowing through the galvanometer is given by ¨ ¨ Voltmeters 18 ¨ ¨ ¨ ¨ A voltmeter is a device that measures the potential difference across its inputs. The voltmeter has very large resistance so that very small amount of current would flow through it, reducing the effect of itself on the circuit. We can construct a voltmeter from a galvanometer connected in series with a large resistance. The current through the galvanometer is given by Ohmmeters 19 ¨ ¨ ¨ An ohmmeter is a device that measures the resistance across its inputs. We can construct an ohmmeter from a galvanometer, a battery, and a resistor, connected in series. Rs is chosen so that when a and b are shorted (negligible resistance), the current through the galvanometer gives a full-scale deflection. 𝐼12 = 4 ℰ 5 647 6489 Example: 3 20 ¨ R = 100 kΩ a) b) If the voltmeter is ideal (infinite internal resistance) what is the measured voltage across R? If the voltmeter has an internal resistance of R V = 600 Ω what is the measured voltage across R?