This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and their absolute errors. The potential difference is V = (18 ± 3) V. So, the measured potential difference is V = 18 V and its absolute error is V = 3 V. The current is I = (5 ± 0.1) A. So, the measured current is I = 5 A and its absolute error is I = 0.1 A. Step 2: Recall the formula for resistance and the rule for propagation of errors in division. According to Ohm's Law, resistance R is given by: R = (V)/(I) When quantities are divided, the maximum fractional error in the result is the sum of the fractional errors of the individual quantities. ( R)/(R) = ( V)/(V) + ( I)/(I) Step 3: Calculate the fractional errors for potential difference and current. Fractional error in potential difference: ( V)/(V) = 3 V18 V = (1)/(6) Fractional error in current: ( I)/(I) = 0.1 A5 A = (1)/(50) Step 4: Calculate the total fractional error in resistance. ( R)/(R) = (1)/(6) + (1)/(50) To add these fractions, find a common denominator, which is 150: ( R)/(R) = (25)/(150) + (3)/(150) = (28)/(150) = (14)/(75) Step 5: Convert the total fractional error to percentage error. Percentage error is the fractional error multiplied by 100\%. Percentage error = ( R)/(R) × 100\% Percentage error = (14)/(75) × 100\% Percentage error = (14 × 4)/(3)\% = (56)/(3)\% Percentage error ≈ 18.666...\% Rounding to one decimal place, the percentage error is 18.7\%. The percentage error in the measurement of resistance of the conductor is 18.7\%. Send me the next one 📸