Question

A 13-cm-long nichrome wire is connected across the terminals of a 1.5 V battery. If the current in the wire is 2.2 A, what is the wire's diameter? Express your answer to two significant figures and include the appropriate units.

Answer 1

The diameter of the nichrome wire connected to a 1.5 V battery can be calculated using the formula for resistance and the area of a circle. The wire's diameter is approximately 0.057 cm.

Step-by-step explanation:

To find the wire's diameter, we can use the formula for the resistance of a wire:

R = (ρ × L) / A

Where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

We can rearrange the formula to solve for the cross-sectional area:

A = (ρ × L) / R

Substituting the given values, we have:

A = (ρ × L) / R = (resistivity × length) / (resistance)

Plugging in the values, we get:

A = (1.1 × 10^-6 Ω·m × 0.13 m) / (2.2 Ω) = 6.318 × 10^-7 m²

Finally, we can use the formula for the area of a circle to find the diameter:

Diameter = 2 × √(A / π)

Plugging in the values, we have:

Diameter = 2 × √(6.318 × 10^-7 / π) = 5.65 × 10^-4 m

Converting to centimeters, the wire's diameter is approximately 0.057 cm.