Physics
Physics
Problem
Two solid cylindrical wires, Wire X and Wire Y, are fabricated from the same metal so their resistivity is identical. The temperature is uniform and constant. • Wire X: length 0.80 m, radius 0.50 mm • Wire Y: length 0.40 m, radius 0.25 mm The two wires are later connected in parallel across an ideal 6.0 V battery. (a) Determine the ratio of the resistances of the two wires. (b) While the wires are connected in parallel to the battery, calculate the ratio of the current in Wire Y to the current in Wire X. (c) For the parallel connection described above, determine the fraction of the total electrical power delivered by the battery that is dissipated in Wire Y. Show all reasoning steps in your answer.Intuitive explanation
Resistance depends on both length and cross-sectional area through . Since Wire X is twice as long but has four times the cross-sectional area (radius squared), it will have half the resistance of Wire Y. When resistors are in parallel, the one with lower resistance carries more current—so you need to find each wire's resistance first, then use to find how the 6.0 V divides the current between them.
Intuitive explanation
Resistance depends on both length and cross-sectional area through . Since Wire X is twice as long but has four times the cross-sectional area (radius squared), it will have half the resistance of Wire Y. When resistors are in parallel, the one with lower resistance carries more current—so you need to find each wire's resistance first, then use to find how the 6.0 V divides the current between them.