Question

Exercise 5 The resistances in this circuit are: Ri battery's emf is 80. V 25 Q, R2 = 11 Q, R3 = 40. 2, R4=72 Q, and Rs = 64 Q. The a) Predict without calculation: which resistors, if any, will have the same current, and which, if any, will have the same voltage? Explain your reasoning. b) [10 points] Calculate the voltage across each of the resistors. For full credit, redraw the circuit each time you replace two or more resistors with their equivalent resistance. R2 R3 R4

Answer 1

Cnivan Ri= 250, R2=11, R 402 R4722, R649 omf 80V RI I R2 R3 I-1' www II www R5 RESEATen RI and R Currunt acnoss are in Sanies Same smce are quivalent rectntoncal and R4 paraite VOltage arenoss OF (Ri and Ra) ane Same as In senies Currant is Same accnoss N.B- riesintors. voltaga tho reeintens across In panailel are ame

R2 R3 ww www www R4 Rs (RRItR) R6 =(25+1 ]2 R3 R4 Re 36-2 R 3 R7 R4 R Ra Rtt Ri 72X36 Rs 72+ 3 6 2592 = 24 106 RB ww R7= 242 Re= R7t R3 24 t 40 640 R6 64 2

80V R3 Re Rs R1- Ret Rs 64 X64 4096 -32 64+64 12 8 Lquvalent rastatante 32 2 30 Riea V= 1R Now 60 - 2.5 mp 32 TOta Curet I - 2.5 amp.

kVL (From appiy IR2+ I,R2tI R B0 I'Rg t (T-IR 80 2 ( I- T')Rs = 80 80 80 - 1.25 I-I 61 Rs I= I-1.25 - à.5-1.as 1.as A 1-25 X40 t .25 T72 80 from eq(2) 50 t 90 -72 I 80 140-B0 60 60 =72 11 72 0. 83 A I 0.83A

Cunrant acnoss Ri 0nd R2 = I, = 0.63 NOw, Vo arcnoss R vOlke't VTIRI= 0.83 X 25 V1 20.75 VOlH voltage ac entass R2 IR2=0.63X 1 9.13 VOlt V2 vo liage acnoss R3 25 X 40 50 VOlt R4 accnoss voltage 4(I-T,) R4 = (1.25-0 63) X 72 0.42 x 72 30.24 V430. 24 Volt 2 acnoss Rs (I-I') Rs= (3-5-1-25] 64 1-25X6t 80 vO 1 Vs 1 N5 B0 Volt