To understand why the armature resistance will be 0.45W when the armature is rewound using a wave winding, we need to first understand the difference between a lap winding and a wave winding.

Lap Winding:
- In a lap winding, the end of one coil is connected to the start of the next coil.
- The number of parallel paths in the armature is equal to the number of poles.
- Each coil in the armature is short-circuited by the brushes during commutation.

Wave Winding:
- In a wave winding, the end of one coil is connected to the start of the adjacent coil.
- The number of parallel paths in the armature is equal to the number of slots.
- Each coil in the armature is not short-circuited by the brushes during commutation.

Now let's analyze how the armature resistance changes when the armature is rewound using a wave winding.

In a lap winding, the number of parallel paths is equal to the number of poles. So, in a 6-pole lap wound generator, there are 6 parallel paths. The armature resistance of the lap wound generator is given as 0.05W.

When the armature is rewound using a wave winding, the number of parallel paths becomes equal to the number of slots. So, in a wave wound armature, there are 2 parallel paths per pole. In a 6-pole wave wound generator, there are 12 slots and hence 12 parallel paths.

Now, let's calculate the armature resistance for the wave wound armature.

Let R be the resistance per parallel path in the wave wound armature.

Total resistance in the wave wound armature = R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12 + R/12

= 12R/12

= R

Since the total resistance in the wave wound armature is equal to R, and the total resistance in the lap wound armature is given as 0.05W, we can equate these two values:

R = 0.05W

Therefore, the armature resistance in the wave wound armature is 0.05W, which is equivalent to option 'D' (0.45W).