A 6-volt battery

(a)

As ,

Let us account for the potential differences when moving from A to C.

(b)

Let the area of cross section of wire be A and resistivity be ρ.

Then,

where V is the voltage across a wire segment of length l.

As, all the quantities except for length are the same for all sections of wire AB,

Hence,

Hence, D is 66.67cm away from A.

(c) As , there is no potential difference across CD and hence, the current through it is zero.

(d)

(a)

As ,

Let us account for the potential differences when moving from A to C.

(b)

Let the area of cross section of wire be A and resistivity be ρ.

Then,

where V is the voltage across a wire segment of length l.

As, all the quantities except for length are the same for all sections of wire AB,

Hence,

This is not possible. As the length of the wire is only 100cm. There is no such point D.

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