Answer: To find the total resistance of the wires, we need to use a formula that takes into account the length and cross-sectional area of the wires and the resistivity of the material they are made of. By plugging in the appropriate values for the length, cross-sectional area, and resistivity of the wires in the formula, we can find the individual resistances of the wires. Then, by using another formula for the total resistance of a parallel combination, we can find the effective resistance of the wires in parallel.
Step-by-step explanation:R = ρ * (L / A)
where R is the resistance of the wire, ρ is the material's resistivity (resistance per unit length), L is the length of the wire, and A is the cross-sectional area of the wire.
according to the given data
AP= 40 cm
px=60cm
Next, we need to calculate the wire PX's length and cross-sectional area. The length is given as 60 cm, and we can assume the same diameter of 1 mm, giving a cross-sectional area of 0.785 mm^2.
Now we can calculate the resistance of each wire using the formula above:
R_AX = ρ * (80 cm / 0.785 mm^2) = 101.91 * ρ
R_PX = ρ * (60 cm / 0.785 mm^2) = 76.43 * ρ
The total resistance of the parallel combination is given by the formula:
1/R_total = 1/R_AX + 1/R_PX
Substituting the values of R_AX and R_PX, we get:
1/R_total = 1/(101.91 * ρ) + 1/(76.43 * ρ)
1/R_total = (1.55 / ρ)
R_total = ρ / 1.55
therefore, the effective resistance of the parallel combination is (ρ / 1.55) ohms