A 1.00 km cable having a cross-sectional area of 0.5 cm? is to be constructed out of equal lengths of copper and aluminium. The resistivity values of copper (Cu) and aluminium (Al) material are pcu = 1.68 x 108 2m and PAI = 2.65 x 108 Qm, respectively. Two designs could be used to make the 1.00 km cable as shown in Figure Q3(a)(i) and Figure Q3(a)(ii). +1.00 km- Cu Al A-0.5 cm2. F1.00 km- Cu ) Al (1) '0.5km 0.5km (ii) (i) Figure Q3(a) (i) First design of the cable is to solder side by side of the two parallel 1.00 km copper and aluminium cables as shown in Figure Q3(a)(i). The cross-sectional areas of copper and aluminium cables are halved of that of the constructed cable. Calculate the total resistance of the cable. (ii) Second design of the cable is to solder a 0.50 km aluminium cable at the end of a 0.50 km copper cable as shown in Figure Q3(a)(ii). Calculate the total resistance of the cable. (iii) Justify which design of the cable gives better electrical performance.

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Publisher:Robert L. Boylestad
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Question 3.
(a)
A 1.00 km cable having a cross-sectional area of 0.5 cm? is to be constructed out of
equal lengths of copper and aluminium. The resistivity values of copper (Cu) and
aluminium (Al) material are pcu = 1.68 x 108 Qm and PAI = 2.65 x 108 Qm,
respectively. Two designs could be used to make the 1.00 km cable as shown in
Figure Q3(a)(i) and Figure Q3(a)(ii).
+1.00 km-
Cu
Al
A-0.5 cm2-
F1.00 km-
O Cu ) Al
0.5 km 0.5km
(i)
(ii)
Figure Q3(a)
(i)
First design of the cable is to solder side by side of the two parallel 1.00 km
copper and aluminium cables as shown in Figure Q3(a)(i). The cross-sectional
areas of copper and aluminium cables are halved of that of the constructed cable.
Calculate the total resistance of the cable.
(ii)
Second design of the cable is to solder a 0.50 km aluminium cable at the end of
a 0.50 km copper cable as shown in Figure Q3(a)(ii). Calculate the total
resistance of the cable.
(iii) Justify which design of the cable gives better electrical performance.
(b)
28.0|V
R
www
4.00 A 6.00 Q
www
6.00 A 3.000
www
Figure Q3(b)
For the circuit shown in Figure Q3(b), determine
(i)
the unknown e.m.f., §.
(ii)
the unknown resistor R.
Transcribed Image Text:Question 3. (a) A 1.00 km cable having a cross-sectional area of 0.5 cm? is to be constructed out of equal lengths of copper and aluminium. The resistivity values of copper (Cu) and aluminium (Al) material are pcu = 1.68 x 108 Qm and PAI = 2.65 x 108 Qm, respectively. Two designs could be used to make the 1.00 km cable as shown in Figure Q3(a)(i) and Figure Q3(a)(ii). +1.00 km- Cu Al A-0.5 cm2- F1.00 km- O Cu ) Al 0.5 km 0.5km (i) (ii) Figure Q3(a) (i) First design of the cable is to solder side by side of the two parallel 1.00 km copper and aluminium cables as shown in Figure Q3(a)(i). The cross-sectional areas of copper and aluminium cables are halved of that of the constructed cable. Calculate the total resistance of the cable. (ii) Second design of the cable is to solder a 0.50 km aluminium cable at the end of a 0.50 km copper cable as shown in Figure Q3(a)(ii). Calculate the total resistance of the cable. (iii) Justify which design of the cable gives better electrical performance. (b) 28.0|V R www 4.00 A 6.00 Q www 6.00 A 3.000 www Figure Q3(b) For the circuit shown in Figure Q3(b), determine (i) the unknown e.m.f., §. (ii) the unknown resistor R.
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