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A balanced 3-phase, 3-wire supply feeds balanced start connected resistors. If one of the resistors is disconnected, the percentage reduction in load will be-
  • a)
    33.33
  • b)
    50
  • c)
    66.67
  • d)
    75
Correct answer is option 'B'. Can you explain this answer?
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A balanced 3-phase, 3-wire supply feeds balanced start connected resi...
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Solution:

Given, a balanced 3-phase, 3-wire supply feeds balanced start connected resistors.

Let the resistance of each resistor be R.

When all three resistors are connected, the current flowing through each resistor is the same.

Therefore, the total current drawn from the supply is 3I, where I is the current flowing through each resistor.

Now, if one of the resistors is disconnected, the circuit becomes unbalanced.

Let's assume that resistor R1 is disconnected.

In this case, the total current drawn from the supply will be 2I, because only two resistors are connected.

Therefore, the percentage reduction in load can be calculated as follows:

Percentage reduction in load = (Current drawn when all three resistors are connected - Current drawn when one resistor is disconnected) / Current drawn when all three resistors are connected x 100

= (3I - 2I) / 3I x 100

= (1/3) x 100

= 33.33%

Therefore, the percentage reduction in load when one resistor is disconnected is 33.33%.

However, the question asks for the percentage reduction in load for the disconnected resistor.

Since there are three resistors, the load on the disconnected resistor is one-third of the total load.

Therefore, the percentage reduction in load for the disconnected resistor is:

Percentage reduction in load for disconnected resistor = (Percentage reduction in load) / 3

= 33.33% / 3

= 11.11%

Therefore, the percentage reduction in load for the disconnected resistor is 11.11%.

However, none of the given options match this answer.

Therefore, we need to re-evaluate our calculations.

When one resistor is disconnected, the remaining two resistors form a voltage divider.

The voltage across each resistor is proportional to its resistance.

Therefore, the current flowing through each resistor will not be the same.

Let's assume that resistor R1 is disconnected.

In this case, the current flowing through resistors R2 and R3 can be calculated as follows:

I2 = (V/√3)/R2

I3 = (V/√3)/R3

where V is the line voltage.

The total current drawn from the supply can be calculated as follows:

I = I2 + I3

= (V/√3) x (1/R2 + 1/R3)

When all three resistors are connected, the current flowing through each resistor is the same.

Therefore, the current flowing through each resistor can be calculated as follows:

I = (V/√3)/R

where R is the resistance of each resistor.

Equating the two expressions for I, we get:

(V/√3)/R = (V/√3) x (1/R2 + 1/R3)

Simplifying, we get:

R = (R2 x R3)/(R2 + R3)

When resistor R1 is disconnected, the load on the remaining two resistors increases.

Therefore, the percentage increase in load can be calculated as follows:

Percentage increase in load = (Load when one resistor is disconnected - Load when all three resistors are connected) / Load when all three resistors are connected x 100

= ((1/R2 + 1/R3) - 1/R) / (1/R) x 100

= ((
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A balanced 3-phase, 3-wire supply feeds balanced start connected resistors. If one of the resistors is disconnected, the percentage reduction in load will be-a)33.33b)50c)66.67d)75Correct answer is option 'B'. Can you explain this answer?
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