In an electrical circuit experiment, the voltage is measured as $V = (100 \pm 5) \mathrm{~V}$ and th

Question

In an electrical circuit experiment, the voltage is measured as $V = (100 \pm 5) \mathrm{~V}$ and the current is measured as $I = (10 \pm 0.2) \mathrm{~A}$. The calculated value of the resistance with its error limits is

Professor PC Thomas Classes · Answer

(b) : Given voltage $V = (100 \pm 5) \mathrm{~V}$ and current $I = (10 \pm 0.2) \mathrm{~A}$. The resistance is $R = \frac{V}{I} = \frac{100}{10} = 10 \Omega$. The maximum fractional error in resistance is given by $\frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} = \frac{5}{100} + \frac{0.2}{10} = 0.05 + 0.02 = 0.07$. The absolute error is $\Delta R = R 	imes 0.07 = 10 	imes 0.07 = 0.7 \Omega$. Thus, the resistance is $(10 \pm 0.7) \Omega$.