A piece of wire of resistance is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is , then the ratio is:
Step 1: Given data
Resistance of wire
Resistance of combination
Step 2: Formula used
Resistance,
is the length of the wire
is the area of cross-section
When connected in parallel, the resistance is given by , where and are resistances of the five parts.
Since is directly proportional to the length of the wire. Therefore the resistance of every part after cutting the wire into parts is .
Step 3: Calculating the ratio,
All the resistances are connected in parallel, let be the equivalent resistance.
Resistance of all resistors
Substituting the values in the formula,
and are resistances of the five parts.
is the resistance of a wire.
Solving further to find the ratio,
So, If the equivalent resistance of this combination is , then the ratio is .
Hence, option D is correct.