A 15m long copper wire has a cross sectional radius of 3mm if 200ma of current flow through the wire. What is the voltage drop of the wire 20⁰c ?

To calculate the voltage drop of the wire, we can use the formula:

V = I * R

Where:
V = Voltage drop
I = Current (200mA = 0.2A)
R = Resistance

The resistance of the wire can be calculated using the formula:

R = ρ * L / A

Where:
ρ = Resistivity of copper (1.68 x 10^-8 ohm*m)
L = Length of the wire (15m)
A = Cross sectional area of the wire (π * r^2)

First, calculate the cross sectional area of the wire:

A = π * (0.003m)^2
A = π * 9 x 10^-6
A = 2.827 x 10^-5 m^2

Now, calculate the resistance of the wire:

R = (1.68 x 10^-8) * 15 / 2.827 x 10^-5
R = 8.95 x 10^-3 ohms

Now, calculate the voltage drop:

V = 0.2 * 8.95 x 10^-3
V = 1.79 volts

Therefore, the voltage drop of the wire at 20⁰C is 1.79 volts.