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The voltage length characteristic of a direct current arc is given by
V= (30 + 60l) volts,
where l is the length of the arc in cm. The power source characteristic is approximated by a straight line with an open circuit voltage = 80 V and a short circuit current = 1000 amp. What is the optimum arc length?
  • a)
    0.5 cm
  • b)
    0.267 cm
  • c)
    0.167 cm
  • d)
    0.34 cm
Correct answer is option 'C'. Can you explain this answer?
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The voltage length characteristic of a direct current arc is given byV...
Given information:
- Voltage-length characteristic of a direct current arc: V = (30 + 60l) volts, where l is the length of the arc in cm.
- Power source characteristic: Straight line with an open circuit voltage = 80 V and a short circuit current = 1000 A.

Objective:
To find the optimum arc length.

Solution:
To find the optimum arc length, we need to determine the point where the power source characteristic line intersects with the voltage-length characteristic curve.

Step 1: Determine the equation of the power source characteristic line.
We are given that the open circuit voltage is 80 V and the short circuit current is 1000 A. The power source characteristic line is approximated to be a straight line.

Using the two given points (0 V, 1000 A) and (80 V, 0 A), we can calculate the slope of the line (m) using the formula:

m = (change in y) / (change in x) = (0 - 1000) / (80 - 0) = -1000 / 80 = -12.5 A/V

So, the equation of the power source characteristic line is:
I = -12.5V + 1000

Step 2: Determine the point of intersection between the power source characteristic line and the voltage-length characteristic curve.
We need to equate the voltage-length characteristic equation with the power source characteristic equation:

(30 + 60l) = -12.5V + 1000

Substituting V = 80 into the equation:
30 + 60l = -12.5(80) + 1000
30 + 60l = -1000 + 1000
30 + 60l = 0
60l = -30
l = -30/60
l = -0.5 cm

Step 3: Determine the optimum arc length.
Since the length of an arc cannot be negative, we discard the negative value and consider the positive value.
Therefore, the optimum arc length is 0.5 cm.

Final Answer:
The optimum arc length is 0.5 cm, which corresponds to option (a).
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The voltage length characteristic of a direct current arc is given byV= (30 + 60l) volts,where l is the length of the arc in cm. The power source characteristic is approximated by a straight line with an open circuit voltage = 80 V and a short circuit current = 1000 amp. What is the optimum arc length?a)0.5 cmb)0.267 cmc)0.167 cmd)0.34 cmCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The voltage length characteristic of a direct current arc is given byV= (30 + 60l) volts,where l is the length of the arc in cm. The power source characteristic is approximated by a straight line with an open circuit voltage = 80 V and a short circuit current = 1000 amp. What is the optimum arc length?a)0.5 cmb)0.267 cmc)0.167 cmd)0.34 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The voltage length characteristic of a direct current arc is given byV= (30 + 60l) volts,where l is the length of the arc in cm. The power source characteristic is approximated by a straight line with an open circuit voltage = 80 V and a short circuit current = 1000 amp. What is the optimum arc length?a)0.5 cmb)0.267 cmc)0.167 cmd)0.34 cmCorrect answer is option 'C'. Can you explain this answer?.
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