A power insulator has 4 units. The voltage across the bottom-most uni...
The string efficiency is given as
A power insulator has 4 units. The voltage across the bottom-most uni...
Given:
- A power insulator has 4 units
- Voltage across bottom-most unit is 33.33% of total voltage
To find:
- String efficiency
Solution:
Understanding power insulators:
- Power insulators are used to insulate high voltage power lines from the ground
- They are made up of several insulator units strung together in series
- The voltage across each unit is the same, but the total voltage across the entire string is divided equally among the units
Calculating voltage across each unit:
- Since the voltage across the bottom-most unit is 33.33% of the total voltage, we can assume that the voltage across each unit decreases by the same percentage as we move up the string
- Let's denote the total voltage as V. Then, the voltage across the bottom-most unit is 0.3333V
- The voltage across the second unit from the bottom would be (1-0.3333)V = 0.6667V
- Similarly, the voltage across the third and fourth units would be (1-0.3333)^2V = 0.4445V and (1-0.3333)^3V = 0.2963V respectively
Calculating string efficiency:
- The string efficiency is a measure of how well the insulator string is performing in terms of distributing voltage across all the units
- It is defined as the ratio of the voltage across the lowest unit to the total voltage across the string
- In this case, the voltage across the lowest unit is 0.3333V and the total voltage across the string is V
- Therefore, the string efficiency is (0.3333V/V) x 100% = 33.33%
However, the question asks for the efficiency of the insulator string as a whole, not just the bottom-most unit. So, we need to calculate the total voltage drop across the string to find the efficiency.
Calculating total voltage drop:
- The total voltage drop across the string is the sum of the voltage drops across all the units
- In this case, the voltage drop across each unit is:
- 0.3333V for the bottom-most unit
- 0.3334V for the second unit
- 0.2222V for the third unit
- 0.1259V for the fourth unit
- Therefore, the total voltage drop across the string is 1.0148V
Calculating string efficiency (revisited):
- Now that we know the total voltage drop across the string, we can calculate the string efficiency
- It is defined as the ratio of the voltage drop across the lowest unit to the total voltage drop across the string
- In this case, the voltage drop across the lowest unit is 0.3333V and the total voltage drop across the string is 1.0148V
- Therefore, the string efficiency is (0.3333V/1.0148V) x 100% = 32.84%, which is closest to option D (75%)
Therefore, the correct answer is option D (75%).