A three-phase full converter charges a battery from a three-phase supply of 230 V. Find the value of the power delivered to the load if a continues current of 20A is flowing through the battery of emf 200 V and internal resistance of 0.5 Ω.a)0 Wb)5600 Wc)4200 Wd)1040 WCorrect answer is option 'C'. Can you explain this answer?

Question

A three-phase full converter charges a battery from a three-phase supply of 230 V. Find the value of the power delivered to the load if a continues current of 20A is flowing through the battery of emf 200 V and internal resistance of 0.5 &#8486;.a)0 Wb)5600 Wc)4200 Wd)1040 WCorrect answer is option 'C'. Can you explain this answer?

Answer

To find the power delivered to the load by a three-phase full converter, we need to calculate the power absorbed by the battery and subtract it from the power supplied by the three-phase supply.

Given:
Three-phase supply voltage (Vph) = 230 V
Battery emf (E) = 200 V
Battery internal resistance (R) = 0.5 Ω
Battery current (I) = 20 A

Calculating the Power Absorbed by the Battery:
The power absorbed by the battery can be calculated using the formula: P = VI

Using Ohm's Law, we can calculate the voltage across the battery terminals:
V = E - IR
V = 200 V - (20 A * 0.5 Ω)
V = 200 V - 10 V
V = 190 V

Now, we can calculate the power absorbed by the battery:
P = VI
P = 190 V * 20 A
P = 3800 W

Calculating the Power Supplied by the Three-Phase Supply:
The power supplied by the three-phase supply can be calculated using the formula: P = √3 * Vph * Iph * cos(ϕ)

Where:
√3 = square root of 3 (constant)
Vph = phase voltage of the three-phase supply
Iph = phase current of the three-phase supply
cos(ϕ) = power factor angle (assumed to be 1 for a purely resistive load)

Since the full converter charges the battery, the current flowing through the load is the same as the battery current, which is 20 A.

Now, we can calculate the power supplied by the three-phase supply:
P = √3 * Vph * Iph * cos(ϕ)
P = √3 * 230 V * 20 A * 1
P = √3 * 230 V * 20 A
P ≈ 7947 W

Calculating the Power Delivered to the Load:
The power delivered to the load is the power supplied by the three-phase supply minus the power absorbed by the battery:
Power delivered to the load = Power supplied by the three-phase supply - Power absorbed by the battery
Power delivered to the load = 7947 W - 3800 W
Power delivered to the load ≈ 4147 W

Since the closest option to 4147 W is 4200 W, the correct answer is option 'C'.

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