Question

Three wires, of the same diameter, are connected in turn between two points maintained at a constant potential difference. Their resistivity's and lengths are rho and L (wire A), 1.2 rho and 1.2L (wire B), and 0.9 rho and L (wire C). Rank the wires according to the rate at which energy is transferred to thermal energy within them, greatest first (use only the symbols > or =, for example B > A = C). ______

Answer 1

Resistance is given by R = PL/A [Where p = resistivity, L = Length, A = Area] For first wire R_1 = P L/A, For second wire R_2 = (1.2P) (1.2L)/A = 1.44PL/A For third wire R_3 = 0.09PL/A = 0.9 PL/A [All wire have same Area] Energy first feed to thermal energy = v^2 /R All the wire are connected to same voltage, thermal energy is inversely - proportional to resistance, For second wire resistance 1.44 PL/A is greater among all three wile so thermal energy through second wile will be smallest among the three wile Third will have smallest resistance 0.9 PL/A so thermal energy through third wire will be greater among all three wire. Rank Third wire (0.9P l) > First wire (P L) > Second wire (1.LP 1.2 L)