Problem Statement:
Two identical DC shunt generators are connected in parallel to share a common load of 500A. The armature resistance is 0.06 ohm and the no-load and terminal voltages are 265V and 250V respectively. Calculate the percentage voltage regulation (w.r.t no-load voltage) of the first generator if the second generator fails to share the load.

Solution:

Step 1: Calculate the armature current of each generator:
Since the generators are connected in parallel, the total load current is 500A. Therefore, each generator will share an equal portion of the load current.

Armature current of each generator = Total load current / Number of generators
= 500A / 2
= 250A

Step 2: Calculate the resistance drop:
Resistance drop in the armature = Armature current * Armature resistance

Resistance drop = 250A * 0.06 ohm
= 15V

Step 3: Calculate the terminal voltage of the first generator:
Terminal voltage = No-load voltage - Resistance drop

Terminal voltage of the first generator = 265V - 15V
= 250V

Step 4: Calculate the percentage voltage regulation:
Percentage voltage regulation = ((No-load voltage - Terminal voltage) / No-load voltage) * 100

Percentage voltage regulation of the first generator = ((265V - 250V) / 265V) * 100
= (15V / 265V) * 100
= 5.66%

Explanation:

When the two identical DC shunt generators are connected in parallel, they share the load current equally. In this case, each generator will share 250A of the total load current. However, when the second generator fails to share the load, the entire load current will be supplied by the first generator.

The armature resistance of the generator causes a voltage drop across it, known as the resistance drop. This drop is determined by the armature current and resistance. In this case, the resistance drop is calculated as 15V.

The terminal voltage of the first generator is the difference between the no-load voltage and the resistance drop. In this case, the terminal voltage of the first generator is calculated as 250V.

The percentage voltage regulation is calculated by comparing the difference between the no-load voltage and the terminal voltage with the no-load voltage. In this case, the percentage voltage regulation of the first generator is calculated as 5.66%.

Therefore, if the second generator fails to share the load, the terminal voltage of the first generator will be 250V, resulting in a percentage voltage regulation of 5.66% with respect to the no-load voltage of 265V.