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If a fixed amount of power is to be transmitted over a certain length with fixed power loss, it can be said that volume of conductor is
  • a)
    inversely proportional to magnitude of the voltage and power factor of the load.
  • b)
    inversely proportional to square of the voltage and square of power factor of theload.
  • c)
    proportional to square of voltage and power factor of the load.
  • d)
    proportional to magnitude of the voltageonly.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If a fixed amount of power is to be transmitted over a certain length ...
Explanation:

To understand why the volume of the conductor is inversely proportional to the square of the voltage and the square of the power factor of the load, we need to consider the power equation and the relationship between power, voltage, current, and resistance.

Power Equation:
The power (P) transmitted through a conductor can be calculated using the following equation:

P = VI cos(θ)

Where:
- P is the power transmitted in watts (W)
- V is the voltage across the conductor in volts (V)
- I is the current flowing through the conductor in amperes (A)
- cos(θ) is the power factor of the load

Relationship between Power, Voltage, Current, and Resistance:
Using Ohm's Law, we know that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance:

I = V/R

Where:
- R is the resistance of the conductor in ohms (Ω)

Volume of Conductor:
Now, let's consider the volume of the conductor. The volume of a conductor is directly proportional to its cross-sectional area (A) and length (L):

Volume = A * L

Inverse Proportion:
From the power equation, we can rewrite it as:

P = (V^2/R) cos(θ)

We can see that the power (P) is inversely proportional to the resistance (R). Since the power loss in the conductor is fixed, we can conclude that the resistance (R) is fixed.

From Ohm's Law, we know that the current (I) is directly proportional to the voltage (V) and inversely proportional to the resistance (R). Therefore, the current (I) is also fixed.

We can rewrite the equation for power (P) as:

P = (I^2 * R) cos(θ)

Since the power (P) and the resistance (R) are fixed, we can conclude that (I^2 * cos(θ)) is also fixed.

Conclusion:
Now, let's consider the volume equation:

Volume = A * L

From the above analysis, we know that (I^2 * cos(θ)) is fixed. We also know that the current (I) is directly proportional to the cross-sectional area (A) of the conductor.

Therefore, if the power loss is fixed, the volume of the conductor (A * L) is inversely proportional to the square of the voltage (V^2) and the square of the power factor (cos^2(θ)) of the load.

Answer:
Hence, the correct answer is option 'B': the volume of the conductor is inversely proportional to the square of the voltage and the square of the power factor of the load.
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If a fixed amount of power is to be transmitted over a certain length with fixed power loss, it can be said that volume of conductor isa)inversely proportional to magnitude of the voltage and power factor of the load.b)inversely proportional to square of the voltage and square of power factor of theload.c)proportional to square of voltage and power factor of the load.d)proportional to magnitude of the voltageonly.Correct answer is option 'B'. Can you explain this answer?
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