A 550V power source provides energy to a load resistance RL through a pair of co
ID: 2141696 • Letter: A
Question
A 550V power source provides energy to a load resistance RL through a pair of copper
(?=1.72x10-8?m) wires that are 20km long. The diameter of the wires is 3.0mm.
During a storm the current, I, supplied by the source increases and the voltage across RL
decreases. An engineer concludes that a fault has developed somewhere along the line and
that there is a shunt resistance RS at some distance x from the source. If the load resistance
is disconnected, I is measured to be 3.8A. When the line terminals at the load are shorted, I
is 7.2A. What is x ?
A. 7.8km
B. 17.9km
C. 14.6km
D. 2.1km
SHOW FULL WORK
Explanation / Answer
? = 550 V, L = 20 km, I1 = 3.8 A, I2 = 7.2 A, d = 3.0 mm, areaA = ?d2/4
Let the resistance of the 2 segments of wires corresponding to xbe
the resistance of the 2 segments of wires corresponding to L - xbe
R2 = ?*2(L - x)/A = 8?(L - x)/(?d2) =8?L/(?d2) - R1
R1 + Rs =?/I1 (1)
so R1 = ?/I1 - Rs
R2 = 8?L/(?d2) - ?/I1 + Rs = Rs -47.405 (2)
R1 + Rs*R2/(Rs + R2) = ?/I2 (3)
(1) - (3):
Rs*[1 - R2/(Rs + R2)] = ?/I1 - ?/I2
Rs2/(Rs + R2) = ?/I1 - ?/I2 =
plug (2) into it,
Rs2/(2Rs - 47.405) = 68.348
Rs2 - 68.348*(2Rs - 47.405) = 0
Rs2 - 136.696Rs + 3240.02 = 0
solve it and get
Rs = 106.18 ?, or 30.514 ?
R1 = ?/I1 - Rs = 38.557 ?, or 114.22 ?
R1 = 8?x/(?d2)
?x = ?d2R1/(8?) = 7.92 km or 23.47km
23.47 > 20, so 23.47 km should be discarded
.
answer: x = 7.92 km
option A
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