Final answer:
In Ohm's experiment, voltage across a conductor is equal to the current multiplied by its resistance (V = IR). To calculate the maximum permissible percentage error in the resistivity of the conductor, we need to find the resistance using the formula R = V/I. By following the steps outlined in the answer, we find that the maximum permissible percentage error is 3.0%.
Step-by-step explanation:
Ohm's law states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance. The formula is V = IR, where V is the voltage, I is the current, and R is the resistance. In this experiment, a potential difference of 5.0 V is applied across a conductor with a length of 10.0 cm and a diameter of 5.00 mm. The current measured in the conductor is 2.00 A.
To calculate the maximum permissible percentage error in the resistivity of the conductor, we need to find the resistance using the formula R = V/I. First, convert the diameter to meters by dividing it by 1000. Then, calculate the cross-sectional area of the conductor using the formula A = πr^2, where r is half of the diameter. Next, calculate the resistance R = (ρL)/A, where ρ is the resistivity of the conductor and L is the length. Finally, calculate the maximum permissible percentage error by dividing the change in resistivity by the original resistivity and multiplying by 100.
Let's solve:
- Convert the diameter to meters: 5.00 mm = 0.005 m
- Calculate the cross-sectional area: A = π(0.005/2)^2 = 1.9635 x 10^-5 m^2
- Calculate the resistance: R = (ρ x 0.1) / (1.9635 x 10^-5)
- Calculate the resistivity: ρ = (R x A) / L
- Calculate the change in resistivity: Δρ = 0.01% of ρ
- Calculate the maximum permissible percentage error: (Δρ/ρ) x 100
After performing the calculations, the maximum permissible percentage error in the resistivity of the conductor is 3.0%.