When a wire of resistance R is cut into three equal parts, each part has resistance R/3. These three parts connected in parallel give an equivalent resistance R₁ = R/9.
Hence, the ratio R₁ : R = 1 : 9.
Science important questions Final Exam 2025 Class 10
Science Question Paper class 10
A wire of total resistance R is divided into three equal parts, so each part has resistance R/3. When these three equal parts are connected in parallel, the reciprocal of the equivalent resistance is the sum of their reciprocals. Hence,
1/R₁ = 3 × (1/(R/3)) = 9/R.
Therefore, the equivalent resistance R₁ = R/9. The ratio of the equivalent resistance to the original resistance is R₁ : R = 1 : 9, showing that resistance decreases nine times.