48. Figure P27.48 shows a circuit model for the transmission of an electrical signal such as cable TV to a large number of subscribers. Each subscriber connects a load resistance R1 between the transmission line and the ground. The ground is assumed to be at zero potential and able to carry any current between any ground connections with negligible resistance. The resistance of the transmission line between the connection points of different subscribers is modeled as the constant resistance Rr. Show that the equivalent resistance across the signal source is R. = (4R,R, +R; )“ +R, Suggestion: Because the number of subscribers is large, the equivalent resistance would not change noticeably if the first subscriber canceled the service. Consequently, the equivalent resistance of the seetion of the circuit to the right of the first load resistor is nearly equal to Req. RT Rr Signal source Figure P27.48

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48. Figure P27.48 shows a circuit model for the transmission of an electrical signal such as cable TV
to a large number of subscribers. Each subscriber connects a load resistance R1 between the
transmission line and the ground. The ground is assumed to be at zero potential and able to carry
any current between any ground connections with negligible resistance. The resistance of the
transmission line between the connection points of different subscribers is modeled as the
constant resistance Rr. Show that the equivalent resistance across the signal source is
R. = (4R,R, +R; )“ +R,
Suggestion: Because the number of subscribers is large, the equivalent resistance would not
change noticeably if the first subscriber canceled the service. Consequently, the equivalent
resistance of the seetion of the circuit to the right of the first load resistor is nearly equal to Req.
RT
Rr
Signal
source
Figure P27.48
Transcribed Image Text:48. Figure P27.48 shows a circuit model for the transmission of an electrical signal such as cable TV to a large number of subscribers. Each subscriber connects a load resistance R1 between the transmission line and the ground. The ground is assumed to be at zero potential and able to carry any current between any ground connections with negligible resistance. The resistance of the transmission line between the connection points of different subscribers is modeled as the constant resistance Rr. Show that the equivalent resistance across the signal source is R. = (4R,R, +R; )“ +R, Suggestion: Because the number of subscribers is large, the equivalent resistance would not change noticeably if the first subscriber canceled the service. Consequently, the equivalent resistance of the seetion of the circuit to the right of the first load resistor is nearly equal to Req. RT Rr Signal source Figure P27.48
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