# Experiment 3: The research of Thevenin theorem

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1 Experiment 3: The reserch of Thevenin theorem 1. Purpose ) Vlidte Thevenin theorem; ) Mster the methods to mesure the equivlent prmeters of liner twoterminl ctive. c) Study the conditions of the mximum output power in the liner twoterminl ctive. 2. Principl nd llustrtion A. Liner twoterminl ctive nd its equivlent circuit. n ny liner twoterminl ctive N S, s shown in Figure 331(), if only studying the externl circuit of the, we cn regrd the s Thevenin equivlent circuit of resistnce nd voltge source in series, s shown in Figure 331(), or Norton equivlent circuit of resistnce nd current source in prllel, s shown in Figure 331(c). S N S R i R i () Liner twoterminl ctive ()Thevenin equivlent circuit (c)norton equivlent circuit Thevenin theorem: Any liner ctive twoterminl lwys cn e replced y voltge nd current source for the externl circuit. The voltge S of voltge source is equl to open circuit voltge of the twoterminl ctive nd its resistnce R i is equl to the equivlent resistnce fter ll independent sources set to e zero. B. Methods to mesure the equivlent prmeters of liner twoterminl ctive s (1) Open circuit voltge method nd short circuit current method se voltmeter to mesure open circuit voltge etween the output terminls of the directly when the output terminls re open connected. Then, use n mmeter to mesure the current SC of the when the output terminls re short connected. The equivlent resistnce of the

2 twoterminl cn e estimted y: (2) Voltgecurrent method = OC SC (331) se voltmeter nd n mmeter to mesure the externl chrcteristic of the twoterminl ctive, s shown in Figure 332. tilize the externl chrcteristic curve to clculte slope tn(φ). The equivlent resistnce of the twoterminl cn e estimted y: Δ = tn ϕ = = (332) Δ f the internl resistnce of twoterminl is very smll, it s not suitle to mesure short circuit current. We cn use voltgecurrent method in this cse, to mesure the open circuit voltge, nd the output voltge N when the current of the twoterminl ctive is fixed to N. The equivlent resistnce of the twoterminl cn e estimted y: SC R eq N = (333) N Δ A ϕ B 0 Δ Figure 332 voltgecurrent chrcteristic of ctive twoterminl SC (3) Hlf voltge method As shown in Figure 333, when lod voltge is hlf of the open circuit voltge of the mesured, the resistnce of lod resistor is equl to the equivlent internl resistnce of the twoterminl ctive. Liner twoterm inl ctive V /2 Figure 333 se hlf voltge method to mesure circuit

3 (4) Zero Method f the twoterminl ctive hs high internl resistnce, using voltmeter to directly mesure it my cuse rther ig error. n this cse, we cn use Zero method to eliminte the effect of the internl resistnce of the Voltmeter. The principl of zero method: compring the twoterminl ctive with voltgestilized source of low internl resistnce, when the output voltge of the voltgestilized source is equl to the open circuit voltge of the twoterminl ctive, the voltmeter shows 0, s shown in figure 334. Then, open the electric circuit nd mesure the output voltge of the voltgestilized source, which is equl to the open circuit voltge of the mesured ctive twoterminl. Liner two termi nl S V Voltge s tilized source ctive Figure 334 se zero method to mesure s 3. Contents nd Steps R 4 510Ω 330Ω S R 3 R 1 10mA R 2 10Ω 510Ω 12V A ma B Thevenin Equivlent circuit S Figure 335 the externl chrcteristic circuit of the twoterminl ctive Figure 336 Thevenin equivlent circuit A. se open circuit voltge method nd short circuit current method to mesure oc nd of the twoterminl ctive As show in Figure 335, the voltgestilized source s nd constntcurrent source s re connected into the liner twoterminl ctive. Open the circuit t lod to get the two terminls A nd B, then, use

4 voltmeter to mesure the voltge AB etween A nd B, nd we will hve = AB. Mesure the current sc when the the circuit is short connected t lod. Record the corresponding voltges nd currents into the Tle 331. Tle 331. The mesured dt for, sc, of the twoterminl ctive (V) SC (ma) = / SC (Ω) B. Mesure the externl chrcteristics of the liner twoterminl ctive As shown in Figure 335, the vrile resistnce ox is connected etween terminls A nd B of the twoterminl ctive. Chnge the resistnce of, s shown in Tle 332, nd mesure the externl chrcteristics of the. Record the corresponding voltges nd currents into the Tle 332. Tle 332. The mesured dt for the externl chrcteristics of ctive twoterminl. (V) (ma) C. Vlidte Thevenin theorem. se vrile resistnce ox nd choose the resistnce equl to the equivlent resistnce, s shown in Step A. Then, connect the vrile resistnce ox nd DC voltgestilized source (equl to the mesured open circuit voltge s shown in Step A ) in series nd construct Thevenin equivlent circuit of the twoterminl ctive, s shown in Figure 336. Chnge the resistnce of, s shown in Tle 333, nd mesure the externl chrcteristics of the. Record the corresponding voltges nd currents into the Tle 333. Tle 333. The mesured dt for the externl chrcteristics of the Thevening equivlent circuit. (V) (ma)

5 D. The study of the conditions of mximum power trnsfer. Bsed on the dt you record in Step C, clculte the power sored y nd record these vlues into Tle 334. Tle 334. The mesured dt for studying the mximum power trnsfer conditions in Thevenin equivlent circuit. P(W) 4. Questions ) Wht is the condition of mesuring sc in the short circuit experiment to otin the Thevenin equivlent circuit? ) Cn we directly short connect the circuit in the experiment? c) Summrize the methods to mesure the open circuit voltge nd equivlent internl resistnce of the twoterminl ctive, nd compre their dvntge nd disdvntge. 5. Writing your reports ) Bsed on the dt you recorded in Step B nd Step C, plot the respective voltgecurrent chrcteristics curves nd vlidte the Thevenin theorem. ) Bsed on the dt you recorded in Step D, plot the curve of power P versus s chnges continully, P = f( ). Vlidte whether the mximum power trnsfer condition is correct or not. n other words, when =, whether the power sored y the lod is the lrgest.

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