A copper wire with a radius of $2.0\mathrm{ mm}$ and a length of $0.80\mathrm{ m}$ is connected across the terminals of a $9.0\mathrm{V}$ battery. How much current flows in the wire?

• A. $1.5\text{kA}$
• B. $2.1\text{kA}$
• C. $2.7\text{kA}$
• D. $5.2\text{kA}$
• E. $12\text{kA}$
• F. $8.3\text{kA}$

Answer: (F)

Verified step by step guidance

1. First, calculate the cross-sectional area of the copper wire. The formula for the area of a circle is A = πr², where r is the radius. Convert the radius from millimeters to meters before substituting into the formula.
2. Next, determine the resistance of the wire using the formula R = ρ(L/A), where ρ is the resistivity of copper (approximately 1.68 × 10⁻⁸ Ω·m), L is the length of the wire, and A is the cross-sectional area calculated in the previous step.
3. Now, apply Ohm's Law, which states V = IR, where V is the voltage, I is the current, and R is the resistance. Rearrange the formula to solve for the current: I = V/R.
4. Substitute the given voltage (9.0 V) and the resistance calculated in step 2 into the rearranged Ohm's Law formula to find the current.
5. Finally, compare the calculated current with the given options to identify the correct answer.