High School

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Three resistors, each having a resistance of 11 Ω, are connected in delta across a three-phase 440 V line. What is the line current?

A. 23.9 A
B. 27.5 A
C. 31.2 A
D. 35.8 A

Answer :

Final answer:

To calculate the line current in a delta configuration for three 11 Ω resistors connected to a 440 V line, the phase voltage is first found and then used to determine the line current. The approximate line current, considering this is a theoretical calculation with potential rounding differences, is 23.1 A. The closest provided option to this calculated value is 23.9 A.the correct answer would be A. 23.9 A

Explanation:

The student is asking about the line current for a three-phase delta connection where each resistor has a resistance of 11 Ω. With a 440 V three-phase line voltage, we'll need to find the phase voltage and then use Ohm's Law to calculate the current through one phase of the delta configuration. This can be challenging since the delta connection complicates the direct application of Ohm's Law as opposed to a star connection.

In a delta connection, the phase voltage (Vph) is not equal to the line voltage (Vline). Instead, Vph is equal to Vline divided by the square root of 3 (Vph = Vline / √3). Once we calculate Vph, we can determine the phase current (Iph), which is the same as the line current (Iline) in a delta connection, by dividing Vph by the resistance value (Iph = Vline / (√3 × R)).

So the phase voltage Vph is 440 V / √3, which is approximately 254 V. The current through one resistor Iph is then 254 V / 11 Ω, which gives us approximately 23.1 A. Since the phase current is the same as the line current in a delta connection, the line current is also 23.1 A. Although this exact figure isn't one of the provided options, the closest answer would be 23.9 A. However, considering rounding discrepancies during calculation, it's important to verify the options provided as they can affect the final answer choice.

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