Question:

A copper wire with a length of 2.0 meters and a cross-sectional area of 4.0 x 10^-6 square meters has a resistance of 0.20 ohms. If a potential difference of 12 volts is applied across the wire, what is the current passing through it?

Answer:

First, we can use the formula for resistance, R, which is given by:

R = ρ * (L/A)

Where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire. Solving for resistivity, ρ, we get:

ρ = R * (A/L)

Now, we can calculate the resistivity of copper:

ρ = 0.20 ohms * (4.0 x 10^-6 m^2 / 2.0 m) = 0.20 ohms * 2 x 10^6 m^-1 = 0.40 x 10^6 ohm * m

We can then use Ohm's Law to find the current passing through the wire. Ohm's Law states:

V = I * R

Where V is the potential difference and I is the current. Solving for I gives us:

I = V / R

Now substituting the given values:

I = 12 V / 0.20 ohms = 60 amperes

Therefore, the current passing through the wire is 60 amperes.