Q2GATE 2020NAT

A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from -5 V to +5 V. The effective thermal voltage, $V_T$ , for the diode is measured to be (29 $\pm$ 2) mV. The resolution of the voltage source in the measurement range is 1 mV. The percentage uncertainty (rounded off to 2 decimal plates) in the measured current at a bias voltage of 0.02 V is _______.

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Q3GATE 2017NAT

The following measurements are obtained on a single phase load: V = 220V $\pm$ 1%, I = 5.0A $\pm$ 1% and W=555W $\pm$ 2%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________.

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📖 Explanation

\begin{aligned} V &= 220 \pm 1\% \\ I&= 5 \pm 1 \%\\ W &=555 \pm 2 \% \\ W&= VI \cos (\phi )\\ p.f. &=\cos (\phi )=\frac{W}{VI} \\ &= \frac{555 \pm 2 \%}{(220 \pm 1\%)(5 \pm 1 \%)}\\ &= \frac{555}{220 \times 5} \pm 4\%\\ p.f.&= 0.5 \pm 4\% \end{aligned}

Q4GATE 2017MCQ

Two resistors with nominal resistance values $R_1 \; and\; R_2$ have additive uncertainties $\Delta R_1$ and $\Delta R_2$ , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

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📖 Explanation

\begin{aligned} \sigma _{res} &= \sqrt{\left ( \frac{\partial R}{\partial R_1} \right )^2 \sigma _1^{2+}\left ( \frac{\partial R}{\partial R_2} \right )^2 \sigma _2^2} \\ &= \sqrt{\left ( \frac{\partial R}{\partial R_1} \right )^2 \Delta R_1^{2+}\left ( \frac{\partial R}{\partial R_2} \right )^2 \Delta R_2^2} \end{aligned}

Q5GATE 2015MCQ

When the Wheatstone bridge shown in the figure is used to find the value of resistor $R_X$ , the galvanometer G indicates zero current when $R_1=50\Omega ,R_2=65\Omega$ and $R_3=100\Omega$ . If $R_3$ is known with $\pm 5$ % tolerance on its nominal value of 100 $\Omega$ , what is the range of $R_X$ in Ohms?

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📖 Explanation

$R_1=50\Omega$ $R_2=60\Omega$ $R_3=100\pm 5%\Omega$ The value of $R_3 \text{with} \pm 5$ % of tollerance,

\begin{aligned} R_3&= 100\pm 5\% \\ &= 100+100 \times \frac{5}{100}=105 \Omega \\ &= 100-100 \times \frac{5}{100}=95 \Omega \end{aligned}

In both condition, the bridge is balance, so under balance condition,

\begin{aligned} \frac{R_1}{R_3}&=\frac{R_2}{R_x} \\ R_x&=\frac{R_2R_3}{R_1} \\ (i) \; \text{when}, \; R_3&=105\Omega \\ \therefore \;\;R_x &= \frac{105 \times 65}{50}=136.50\Omega \\ (ii)\; \text{when}, \; R_3&=95 \Omega \\ \therefore \;\;R_x &= \frac{95 \times 65}{50}=123.50\Omega \end{aligned}

Q6GATE 2009MCQ

The measurement system shown in the figure uses three sub-systems in cascade whose gains are specified as $G_1,G_2 \; and \; \frac{1}{G_3}$ . The relative small errors associated with each respective subsystem $G_1,G_2 \; and \; G_3$ are $\varepsilon _1,\varepsilon _2 \; and \; \varepsilon _3$ . The error associated with the output is :

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📖 Explanation

$\frac{dG_1}{G_1}=\varepsilon _1,$ $\frac{dG_2}{G_2}=\varepsilon _2,$ and $\frac{dG_3}{G_3}=\varepsilon _3$ Output $(y)_0=\frac{G_1G_3}{G_3}x$ where, $\;\; x=input$ $\ln y=\ln G_1+ \ln G_2- \ln G_3 +\ln x$ Differentiating both side, $\frac{dy}{y}=\frac{dG_1}{G_1}+\frac{dG_2}{G_2}-\frac{dG_3}{G_3}+\frac{dx}{x}$ No error is specified in input, so $\frac{dx}{x}=0$ $\frac{dy}{y}==\varepsilon _1+\varepsilon _2-\varepsilon _3$

Q7GATE 2006MCQ

A variable w is related to three other variables x, y, z as w=xy/z. The variables are measured with meters of accuracy $\pm$ 0.5% reading, $\pm$ 1% of full scale value and $\pm$ 1.5% reading. The actual readings of the three meters are 80, 20 and 50 with 100 being the full scale value for all three. The maximum uncertainty in the measurement of w will be

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📖 Explanation

Full scale reading of all three =100 Reading of x =80 Reading of y =20 Reading of z =50 $\delta x=\pm 0.5$ % of reading $=\pm \frac{0.5 \times 80}{100}=\pm 0.4$ $\delta y=\pm 1$ % of reading $=\pm \frac{1 \times 100}{100}=\pm 1$ $\delta z=\pm 1.5$ % of reading $=\pm \frac{1.5 \times 50}{100}=\pm 0.75$ Given $\omega =\frac{xy}{z}$ taking log, we get, $\log \omega = \log x +\log y - \log z$ differenting w.r.t. $\omega$ we get $\frac{\delta \omega }{\omega }=\frac{\delta x}{x}+\frac{\delta y}{y}-\frac{\delta z}{z}$ For maximum limiting error, $\frac{\delta \omega }{\omega }=\pm \left ( \frac{0.4}{80}+\frac{0.1}{20}+\frac{0.75}{100} \right ) \times 100=\pm 7%$

Q8GATE 2001MCQ

Resistances $R_{1}$ and $R_{2}$ have, respectively, nominal values of 10 $\Omega$ and 5 $\Omega$ , and tolerances of $\pm 5$ % and $\pm 10$ %. The range of values for the parallel combination of $R_{1}$ and $R_{2}$ is

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📖 Explanation

Range of $R_1=10\pm 10 \times \frac{5}{100}$ $\;\;= 9.5\Omega \text{to} 10.5\Omega$ Range of $R_2=5\pm 5 \times \frac{10}{100}$ $\;\;= 4.5\Omega \text{to} 5.5\Omega$ $\because \;\; R_p=\frac{R_1R_2}{R_1+R_2}$ $\therefore$ Range of $R_p=\frac{9.5 \times 4.5}{9.5+4.5} \text{to} \frac{10.5 \times 5.5}{10.5+5.5}$ $\;\;=3.05\Omega \text{to} 3.61 \Omega$

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