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
It is given that a piece of wire of resistance is cut into five equal parts. These parts are then connected in parallel.
The equivalent resistance of the combination is .
Step 2: Formula used
Resistance is the opposition that an electrical device has to the flow of electrical current. It is represented by symbol .
The formula to find the resistance is,
Here, is the resistivity, is the length of wire and is the cross sectional area.
Step 3. Find the ratio of .
The resistance is directly proportional to length of the wire.
Thus, the resistance of each five parts after cutting the wire is,
When all the resistances are connected in parallel,
Let us consider, is the equivalent resistance.
Now, we will find the ratio of .
We will find the ratio of .
The ratio of is .
Hence, option is correct answer.