Question

A three-phase circuit has two parallel balanced ∆ loads, one of 33-Ω resistors and one of 47-Ω resistors. Find the magnitude of the total line current when the line-to-line voltage is 220 V rms.

Answer 1

To determine the total line current in the given three-phase circuit, calculate the phase current for each resistor load, then multiply by √3 to find line currents, and finally add them together since the loads are in parallel.

Step-by-step explanation:

To find the magnitude of the total line current in a three-phase circuit with two parallel balanced Δ loads, we must first calculate the current through each load and then combine them

For the 33-Ω resistor load in a Δ configuration, the phase voltage (Vph) is equal to the line-to-line voltage (VLL) divided by √3, which is 220 V / √3. The phase current (Iph) for a Δ connection is Vph / R. Therefore, Iph for the 33-Ω load is (220 V / √3) / 33 Ω. Similarly, we calculate Iph for the 47-Ω load. The total line current, Iline, for each load in a Δ connection is √3 times the phase current because Iline = Iph √3 for Δ connections.

To calculate the total line current of the system, we add the line currents of both loads since the loads are in parallel. Hence, the total line current is the sum of the currents for the 33-Ω load and the 47-Ω load.

Answer 2

To calculate the total line current in a three-phase circuit with parallel balanced Δ loads of 33-Ω and 47-Ω resistors and a 220 V rms line-to-line voltage, calculate the per-phase voltage, determine the phase currents using Ohm's law, calculate the line current for each set of resistors as the phase current multiplied by √3, and then sum these line currents.

Step-by-step explanation:

To find the magnitude of the total line current in a three-phase circuit with two parallel balanced Δ loads, one comprised of 33-Ω resistors and one with 47-Ω resistors, given a line-to-line voltage of 220 V rms, we first calculate the phase current for each set of resistors and then determine the total line current.

Here are the steps for the calculation:

• Calculate the per-phase voltage: The per-phase voltage (line-to-neutral) is V_Phase = Voltage_line-to-line / √3, which in this case is 220 V / √3.
• Calculate the current for each Δ-connected resistor set using Ohm's law (I = V/R): Since the resistors are in a delta (Δ) configuration, the voltage across each resistor is the phase voltage we just calculated. Therefore, for each set of resistors, I_33ohm = V_Phase / 33 Ω and I_47ohm = V_Phase / 47 Ω.
• Calculate the line current: The line current in a Δ-connected load is equal to the phase current multiplied by √3. So for each set of resistors, I_line_33ohm = I_33ohm * √3 and I_line_47ohm = I_47ohm * √3.
• Sum the line currents: The total line current is the sum of the line currents for each set of resistors, I_total = I_line_33ohm + I_line_47ohm.

Using these steps, you can calculate the total line current for the circuit when supplied by a 220 V rms line-to-line voltage.