0.75 A current flows through an iron wire when a battery of 1.5 volts is connected across its ends. The length of the wire 5.0 m and its cross-sectional area is 2.5 x 10^-7 m2. What is the resistivity of iron?
Correct answer: E. 1.0 x 10^-7 Ωm
- A. 9.0 x 10^-7 Ωm
- B. 7.0 x 10^-7 Ωm
- C. 5.0 x 10^-7 Ωm
- D. 3.0 x 10^-7 Ωm
- E. 1.0 x 10^-7 Ωm
Explanation
To solve this problem, start by using Ohm's law, V = IR, to find the resistance (R). Given V = 1.5 V and I = 0.75 A, R = V/I = 1.5 V / 0.75 A = 2 Ω.Next, use the formula for resistivity (resistivity = R × A / l), where A is the cross-sectional area (2.5 × 10-7 m2) and l is the length of the wire (5.0 m). Plugging in the values, resistivity = 2 Ω × (2.5 × 10-7 m2) / 5.0 m = 1.0 × 10-7 Ωm.Thus, the correct answer is 1.0 x 10-7 Ωm. The other options result from errors in applying the formulas or calculations.
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