A piece of wire of resistance R and cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R1 then the ratio of R and R1 is what.
R = R
R1 = R/5*5 = R/25
So (R/R1) = (R/R/25) = R*25/R = 25
To find the equivalent resistance of resistors connected in parallel, you can use the formula:
1/R1 = 1/R2 + 1/R3 + ... + 1/Rn
where R1 is the equivalent resistance and R2, R3, ..., Rn are the individual resistances.
In this case, the wire is cut into five equal parts, so each part has a resistance of R/5. When these parts are connected in parallel, the equivalent resistance, R1, can be found as:
1/R1 = 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5)
Simplifying the above expression:
1/R1 = 5/((R/5)) = 5 * 5/R = 25/R
To find the ratio of R and R1, divide R1 by R:
R/R1 = R/(25/R) = R * R/25 = R^2/25
Therefore, the ratio of R and R1 is R^2/25.