**[1994 1M]** A precise measurement guarantees accuracy of the measured quantity.[True/False]

Ans: False.

**Explanation:**

A precise measurement is attempted as close as accurate but it does not guarantee the accuracy.

**[1995 : 1 M]** Four ammeters M1, M2, M3 and M4 with the following specifications are available.

Instrument | Type | Full scale value (A) | Accuracy % of FS |

M_{1} | 3\frac{1}{2} digit dual slope | 20 | Â±0.10 |

M_{2} | PMMC | 10 | Â±0.20 |

M_{3} | Electro-dynamic | 5 | Â±0.50 |

M_{4} | Moving-iron | 1 | Â±1.00 |

A current of 1 A is to be measured. To obtain minimum error in the reading, one should select meter.

(a) M1

(b) M2

(c) M3

(d) M4

Ans: (d)

**Explanation:**

Error in the measuring instrument is estimated as the product of Full Scale Deflection and Accuracy.

Error in Reading = FSD Ã— Accuracy

Hence, error in reading of first meter = 20 \times \frac{\pm 0.1}{100}= \pm 0.02

Error in reading of second meter = 10 \times \frac{\pm 0.2}{100}= \pm 0.02

Error in reading of third meter = 5 \times \frac{\pm 0.5}{100}= \pm 0.025

Error in reading of fourth meter = 1 \times \frac{\pm 1.00}{100}= \pm 0.01

Fourth meter has least error, hence it would be the choice.

**[1999 : 2 M]** A current of \left [ 2+\sqrt{2}\; sin (sin\; 314t+30^{o})+2+\sqrt{2} cos (952t+45^{o})\right ] A is measured with a thermocouple type, 5A full scale, class-1 meter. The meter reading would lie in the range,

(a) 5 A Â± 1%

(b) (2+3\sqrt2)A\pm1\%

(c) 3 A Â± 1.67%

(d) 2 A Â± 0.5%

Ans. (c)

**Explanation:**

We know that, thermocouple type instruments read RMS values. Hence the meter reading is nothing but the RMS value of the current.

I_{rms}=\sqrt{2^{2}+\left ( \frac{\sqrt{2}}{\sqrt{2}} \right )^{2}+\left ( \frac{2\sqrt{2}}{\sqrt{2}} \right )^{2}}= \sqrt{4+1+4}

Hence, I_{RMS} = 3A

Given meter is class 1 meter and for class 1 meter, accuracy is 1% for full scale range i.e. for 5 A.

Hence, for 3A, accuracy would be around 5/3 % = 1.67 %

**[2001 : 2 M]** Resistance R_{1} and R_{2}, have, respectively, nominal values of 10Î© and 5Î© and tolerances of Â±5% and Â±10%. The range of values for the parallel combination of R_{1} and R_{2} is_______.

(a) 3.077 Î© to 3.636 Î©

(b) 2.805 Î© to 3.371 Î©

(c) 3.237 Î© to 3.678Î©

(d) 3.192 Î©* *to 3.435 Î©

Ans. (a)

**Explanation:**

As we are given the tolerances for each resistance, let us find out their ranges. And considering lower and upper limits separately we can find the range for their parallel combination.

Range of R_{1} = 10\pm 10\times \frac{5}{100} = 9.5Î© to 10.5Î©

Range of R_{2}= 5\pm 5\times \frac{10}{100}=4.5Î© to 5.5 Î©

Therefore, Range for R_{p}

**[2006: 2 M]** A variable w is related to three other variables x, y, z as w = xy/z. The variables are measured with meters of accuracy Â± 0.5% reading, Â± 1% of full scale value and Â±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 limiting error in the measurement of w will be______.

a) Â±0.5 % rdg

b) Â±5.5% rdg

c) Â±6.7% rdg

d) 7.0% rdg

Ans. (d)

**Explanation:**

From the given data we can find the errors encountered while taking the readings.

Full scale readings of all three meters are 100 each. While, readings of x=80, readings of y=20 and readings of z=50

Î´x=Â±0.5 % of reading= \pm \frac{0.5\times 80}{100} =Â±0.4.

Î´y=Â±1 % of full reading= \pm \frac{1\times 100}{100} =Â±1.

Î´z=Â±1.5 % of reading= \pm \frac{1.5\times 50}{100} =Â±0.75.

Given that, w=\frac{xy}{z}

taking log, we get

log w= log x + log y – log z

differentiating w.r.t Ï‰ we get

\frac1\omega=\frac1x\frac{\delta x}{\delta\omega}+\frac1y\frac{\delta y}{\delta\omega}-\frac1z\frac{\delta z}{\delta\omega} \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{1}{20}+ \frac{0.75}{100}\right )\times 100Hence, Ans = Â±7 %

**[2015 : 1 M, Set-1]** When the Wheatstone bridge shown in the figureÂ is used to find the value of resisto*r R _{x}, *the galvanometer G indicates zero current when

(a) [123.50, 136.50]

(b) [125.89, 134.12]

(c) [117.00, 143.00]

(d) [120.25, 139.75]

Ans. (a)

**Explanation:**

R_{1}=50Î© and R_{2}=65Î©

The value of R_{3 }is given with Â±5% tolerance over the nominal value

âˆ´ R_{3}=100 Â± [5% of 100]

or, R_{3}=100 - 100\times \frac{5}{100}=95\Omega

In both conditions, the bridge is balanced,

\frac{R_{1}}{R_{3}}=\frac{R_{2}}{R_{x}} R_{x}=\frac{R_{2}R_{3}}{R_{1}}So, let us find range for R_{3} by considering range for R_{x}

i) when R_{3}=105Î©

R_{x}=\frac{105\times 65}{50} =136.50Î©

ii) when R_{3}=95Î©

R_{x}=\frac{95\times 65}{50} =123.50Î©

**[2017: 1 M, Set-1]** The following measurement are obtained on a single phase load: V = 220 V Â±1%*. I = *5.0 A Â± 1% and W=555 *W *Â± 2%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ____ (Give answer up to one decimal place.)

Ans. 0.5 Â± 4 %

**Explanation:**

We know that, W=VÃ—IÃ—cos (Î¦)

p.f= cos (\phi )=\frac{W}{V.I} \therefore P.F.=\frac{555\pm2\%}{(220\pm1\%)(5\pm1\%)}=\frac{555}{220\times5}\pm4\%Hence, p.f=cos(Î¦)=0.5 Â±4%

**[2017: 1 M, Set-2]** Two resistors with nominal resistance values *R _{1}, *and R

a) \pm \sqrt{\left ( \frac{\partial R}{\partial R_{1}} \bigtriangleup R_{1}\right )^{2} +{\left ( \frac{\partial R}{\partial R_{2}} \bigtriangleup R_{2}\right )}^{2}}

b) \pm \sqrt{\left ( \frac{\partial R}{\partial R_{2}} \bigtriangleup R_{1}\right )^{2} +{\left ( \frac{\partial R}{\partial R_{1}} \bigtriangleup R_{2}\right )}^{2}}

c) \pm \sqrt{\left ( \frac{\partial R}{\partial R_{1}}\right )^{2} \bigtriangleup R_{2} +{\left ( \frac{\partial R}{\partial R_{2}} \right )}^{2}\bigtriangleup R_{1}}

d) \pm \sqrt{\left ( \frac{\partial R}{\partial R_{1}}\right )^{2} \bigtriangleup R_{1} +{\left ( \frac{\partial R}{\partial R_{2}} \right )}^{2}\bigtriangleup R_{2}}

Ans. (a)

**Explanation:**

Login

Accessing this course requires a login. Please enter your credentials below!