Question

A 20-cm-long nichrome wire is connected across the terminals of a 1.5 V battery.

Part A

What is the current density inside the wire?

Part B

If the current in the wire is 2.0 A , what is the wire's diameter?

Answer 1

onsider the given data; Length of the wire, L = 20 cm Voltage of battery, V-15V 0.2 m Standard resistivity for nichrome wire, ρ-1.5x10-6 Ω-m Write the expression for the current density Here. J is the current density and is the cross-section area of the wire Write the expression for current Here, R is the resistance of the wire Write the expression for the resistance of wire R-PL Here, p is the resistivity of wire.

From equation (1). (2) and (3) we get Substitute the values in the above equation 1.5 1.5x10x0.2 0.2×10-6 -5x10 A/m Hence, the current density inside the wire is 5x10° A/m The current in the wire I 2.0 A Write the expression to detemine the diameter of the wire

41 41 Here, d is the diameter of the wire. Substitute the values in the above equation 4 x2 3.14x(5x106 V15.7x10% 7.138x10-m 0.071 cm Hence, the diameter of the wire is 0.071 cm