A student wants to check the resistance of a resistor by measuringthe voltage across it (V) and the resulting current through it (I)and then calculating the resistance R=V/I. He measures fourdifferent values of V and the corresponding currents I, asfollows:
Voltage, V (volts): 11.2 13.4 15.1 17.7
Current, I (amps): 4.67 5.46 6.28 7.22
(a) Calculate the four corresponding values of R (which will comeout in ohms). What is his best estimate for R, and what is therandom component of its uncertainty (delta_Rrandom)?
(b)The resistor is rated at 2.50 ohms, which does not lie withinthe range R_best + or - deltaR_random, so he considers thepossibility that the voltmeter and ammeter suffer some systematicerror. The lab technician states that many of the meters in the labhave up to a 2 percent systematic error. Use error propagation tofind the possible systematic error in R, and then combine thesystematic and random errors to give the total uncertainty. (Inboth calculations, combine errors in quadrature.) What is his finalanswer and how does it compare with the given value?
A student wants to check the resistance of a resistor by measuringthe voltage across it (V) and the resulting current through it (I)and then calculating the resistance R=V/I. He measures fourdifferent values of V and the corresponding currents I, asfollows:
Voltage, V (volts): 11.2 13.4 15.1 17.7
Current, I (amps): 4.67 5.46 6.28 7.22
(a) Calculate the four corresponding values of R (which will comeout in ohms). What is his best estimate for R, and what is therandom component of its uncertainty (delta_Rrandom)?
(b)The resistor is rated at 2.50 ohms, which does not lie withinthe range R_best + or - deltaR_random, so he considers thepossibility that the voltmeter and ammeter suffer some systematicerror. The lab technician states that many of the meters in the labhave up to a 2 percent systematic error. Use error propagation tofind the possible systematic error in R, and then combine thesystematic and random errors to give the total uncertainty. (Inboth calculations, combine errors in quadrature.) What is his finalanswer and how does it compare with the given value?
