Question

Two wires P and Q are made from the same material. Wire P and Q has length in the ratio of 18:12 and having cross sectional area in the ratio of 4:3. Then ration of their resistances is:

(A) 8:9
(B) 9:8
(D) 2:1
(C) 1:2​

Answer 1

The ratio of the resistances of two wires P and Q, made from the same material, with lengths in the ratio 18:12 and cross-sectional areas in the ratio 4:3, is 9:8.

Step-by-step explanation:

The resistance of a wire depends on its length, cross-sectional area, and resistivity. In this case, wires P and Q are made from the same material, so their resistivities are equal. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Therefore, the ratio of their resistances is equal to the ratio of their lengths multiplied by the inverse ratio of their cross-sectional areas.

Let's assume the length of wire P is 18x and the length of wire Q is 12x. The cross-sectional area of wire P is 4a and the cross-sectional area of wire Q is 3a.

The ratio of their resistances is (length of P ÷ length of Q) × (cross-sectional area of Q ÷ cross-sectional area of P). Substituting the values, we get:

(18x ÷ 12x) × (3a ÷ 4a) = 3/2 × 3/4 = 9/8