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As shown in Figure 1 below, a circuit of resistances R1 and R2 extends to infinity to the right. 8. in and R R2 R2 so on ww R, R, R, Figure 1 (a) Show that the total resistance Rr of the infinite circuit (i.e. the resistance between points a and b) is equal to Rr = R1 + JR,? + 2R,R2 (Hint: Because the circuit is infinite, the resistance of the network to the right of the points c and d can also be treated as being equivalent to Rr.) (b) Show that if the potential difference between the points a and b in Figure 1 above is Vab, then the potential difference between the points c and d is Ved where Ved = Vab and B (1+B) 2R; (RT+R;) RTR2

As shown in Figure 1 below, a circuit of resistances R1 and R2 extends to infinity to the right. 8. in and R R2 R2 so on ww R, R, R, Figure 1 (a) Show that the total resistance Rr of the infinite circuit (i.e. the resistance between points a and b) is equal to Rr = R1 + JR,? + 2R,R2 (Hint: Because the circuit is infinite, the resistance of the network to the right of the points c and d can also be treated as being equivalent to Rr.) (b) Show that if the potential difference between the points a and b in Figure 1 above is Vab, then the potential difference between the points c and d is Ved where Ved = Vab and B (1+B) 2R; (RT+R;) RTR2

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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8. As shown in Figure 1 below, a circuit of resistances R1 and R2 extends to infinity to the right. R, R, and R R R2 so on R, R, R, Figure 1 (a) Show that the total resistance R of the infinite circuit (i.e. the resistance between points a and b) is equal to Rr = R1 + R, + 2R, R2 (Hint: Because the circuit is infinite, the resistance of the network to the right of the points c and d can also be treated as being equivalent to Rr.) (b) Show that if the potential difference between the points a and b in Figure 1 above is Vab, then the potential difference between the points c and d is Ved where Vca =Yab and B = 2R; (R7+R2) (1+B) RTR2 (c) n= 1, segment of the circuit which extends for an infinite number of segments to the right. Show that the potential difference between the upper and lower wires n segments from the left-hand end is Note that for the purposes of this question, the points c and d are the first, or Vab (1 + B)" (d) If R; = R2, show how many segments n are needed to reduce the potential difference Vn to 1% of Vo?
Transcribed Image Text:8. As shown in Figure 1 below, a circuit of resistances R1 and R2 extends to infinity to the right. R, R, and R R R2 so on R, R, R, Figure 1 (a) Show that the total resistance R of the infinite circuit (i.e. the resistance between points a and b) is equal to Rr = R1 + R, + 2R, R2 (Hint: Because the circuit is infinite, the resistance of the network to the right of the points c and d can also be treated as being equivalent to Rr.) (b) Show that if the potential difference between the points a and b in Figure 1 above is Vab, then the potential difference between the points c and d is Ved where Vca =Yab and B = 2R; (R7+R2) (1+B) RTR2 (c) n= 1, segment of the circuit which extends for an infinite number of segments to the right. Show that the potential difference between the upper and lower wires n segments from the left-hand end is Note that for the purposes of this question, the points c and d are the first, or Vab (1 + B)" (d) If R; = R2, show how many segments n are needed to reduce the potential difference Vn to 1% of Vo?
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