The-resistance-R-of-an-unknown-resistor-is-found-by-measuring-the-potential-difference-V-across-the-resistor-and-the-current-I-through-it-and-using-the-equation-R-V-I-The-voltmeter-reading-has-a-3

Question Number 33272 by NECx last updated on 14/Apr/18

$${The}\:\boldsymbol{{resistance}}\:\boldsymbol{{R}}\:\boldsymbol{{of}}\:\boldsymbol{{an}}\: \\ $$$$\boldsymbol{{unknown}}\:\boldsymbol{{resistor}}\:\boldsymbol{{is}}\:\boldsymbol{{found}}\:\boldsymbol{{by}} \\ $$$$\boldsymbol{{measuring}}\:\boldsymbol{{the}}\:\boldsymbol{{potential}} \\ $$$$\boldsymbol{{difference}}\:\boldsymbol{{V}}\:\boldsymbol{{across}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{resistor}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{current}}\:\boldsymbol{{I}}\:\boldsymbol{{through}} \\ $$$$\boldsymbol{{it}}\:\boldsymbol{{and}}\:\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{equation}}\:\boldsymbol{{R}}=\frac{{V}}{{I}}. \\ $$$$\boldsymbol{{The}}\:\boldsymbol{{voltmeter}}\:\boldsymbol{{reading}}\:\boldsymbol{{has}}\:\boldsymbol{{a}}\:\mathrm{3\%} \\ $$$$\boldsymbol{{uncertainty}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{ammeter}} \\ $$$$\boldsymbol{{reading}}\:\boldsymbol{{has}}\:\boldsymbol{{a}}\:\mathrm{2\%}\:\boldsymbol{{uncertainty}}. \\ $$$$\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{uncertainty}}\:\boldsymbol{{in}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{calculated}}\:\boldsymbol{{resistance}}? \\ $$

Commented by NECx last updated on 14/Apr/18

$${please}\:{help} \\ $$

Answered by MJS last updated on 14/Apr/18

$${R}=\frac{\mathrm{1}.\mathrm{03}{V}}{.\mathrm{98}{I}}\approx\mathrm{1}.\mathrm{05}\frac{{V}}{{I}} \\ $$$${R}=\frac{.\mathrm{97}{V}}{\mathrm{1}.\mathrm{02}{I}}\approx.\mathrm{95}\frac{{V}}{{I}} \\ $$$$\mathrm{so}\:\mathrm{the}\:\mathrm{uncertainty}\:\mathrm{in}\:{R}\:\mathrm{is}\:\mathrm{5\%} \\ $$$$ \\ $$$$\mathrm{with}\:\mathrm{both}\:\mathrm{division}\:\mathrm{and}\:\mathrm{multiplication} \\ $$$$\mathrm{the}\:\mathrm{resulting}\:\mathrm{uncertainty}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{single}\:\mathrm{uncertainties} \\ $$

Commented by NECx last updated on 14/Apr/18

$${Thanks}\:{so}\:{much} \\ $$

Commented by NECx last updated on 14/Apr/18

$${This}\:{what}\:{I}\:{did}\:{tho}\:{I}\:{dont}\:{know} \\ $$$${what}\:{went}\:{wrong} \\ $$$$ \\ $$$${R}=\frac{{V}}{{I}}\:\rightarrow\:\frac{{dR}}{{R}}=\frac{{dV}}{{V}}\:−\:\frac{{dI}}{{I}} \\ $$$$ \\ $$$${dR}={R}\left(\frac{{dV}}{{V}}−\frac{{dI}}{{I}}\right) \\ $$$${dV}=\mathrm{3\%}{V}\:\:{dI}=\mathrm{2\%}{I} \\ $$$${dR}={R}\left(\mathrm{3\%}−\mathrm{2\%}\right) \\ $$$$ \\ $$$${dR}=\mathrm{1\%}{R} \\ $$$$ \\ $$$${please}\:{whats}\:{wrong} \\ $$

Commented by MJS last updated on 14/Apr/18

$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:+\mathrm{3\%}\:\mathrm{and}\:+\mathrm{2\%},\: \\ $$$$\mathrm{it}'\mathrm{s}\:\pm\mathrm{3\%}\:\mathrm{and}\:\pm\mathrm{2\%}\:\Rightarrow \\ $$$$\Rightarrow\:{dV}=\mathrm{3\%}\:\mathrm{or}\:{dV}=−\mathrm{3\%} \\ $$$$\:\:\:\:\:\:\:{dI}=\mathrm{2\%}\:\mathrm{or}\:{dI}=−\mathrm{2\%} \\ $$$$\mathrm{with}\:\mathrm{my}\:\mathrm{method}: \\ $$$$\mathrm{it}\:\mathrm{could}\:\mathrm{be}\:\frac{\mathrm{1}.\mathrm{03}{V}}{\mathrm{1}.\mathrm{02}{I}}\:\mathrm{or}\:\frac{.\mathrm{97}{V}}{.\mathrm{98}{I}}\:\mathrm{but} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{higher},\:\mathrm{as}\:\mathrm{I} \\ $$$$\mathrm{showed}\:\mathrm{above} \\ $$$$ \\ $$

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