Previous Year Questions- Characteristics of Instruments and Measurement Systems -

Q1: 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 ± 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 _______.  (2020)
(a) 5.87
(b) 2.35
(c) 11.5
(d) 9.2
Ans: (c)

Q2: Two resistors with nominal resistance values R₁ and R₂ have additive uncertainties ΔR₁ and ΔR₂, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is  (SET-2 (2017))
(a)
(b)
(c)
(d)
Ans: (a)
Sol: 
Q3: The following measurements are obtained on a single phase load:
V = 220V ± 1%, I = 5.0A ± 1% and W = 555W ± 2%.
If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________.  (SET-1(2017))
(a) 20%
(b) 40%
(c) 4%
(d) 0.40%
Ans: (c)
Sol: V = 220 ± 1%
I = 5 ± 1%
W = 555 ± 2%
W = VI cos(∅)
p.f. = cos(∅) = (W/VI)
p.f. = 0.5 ± 4%

Q4: 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 R₁ = 50Ω, R₂ = 65Ω and R₃ = 100Ω. If R₃ is known with ±5% tolerance on its nominal value of 100 Ω , what is the range of R_X in Ohms? (SET-1 (2015))
(a) [123.50, 136.50]
(b) [125.89, 134.12]
(c) [117.00, 143.00]
(d) [120.25, 139.75]
Ans: (a)
Sol: R₁ = 50Ω
R₂ = 60Ω
R₃ = 100 ± 5
The value of R₃ with ±5% of tollerance,
R₃ = 100 ± 5%
= 100 + 100 × (5/100) = 105Ω
= 100 − 100 × (5/100) = 95Ω
In both condition, the bridge is balance, so under balance condition,

Q5: The measurement system shown in the figure uses three sub-systems in cascade whose gains are specified as G₁, G₂ and (1/G₃). The relative small errors associated with each respective subsystem G₁, G₂ and G₃ are ε₁, ε₂ and ε₃. The error associated with the output is : (2009)
(a) $\epsilon 1+\epsilon 2+1/\epsilon 3$ε₁ + ε₂ + 1/ε₃
(b) ε₁ε₂/ε₃
(c) $\epsilon 1+\epsilon 2-\epsilon 3$ε₁ + ε₂ − ε₃ 
(d) $\epsilon 1+\epsilon 2+\epsilon 3$ε₁ + ε₂ + ε₃ 
Ans: (c)
Sol: where, x = input
ln⁡ y = ln⁡ G₁ + ln⁡ G₂−ln⁡ G₃ + ln⁡ x
Differentiating both side,
No error is specified in input, so (dx/x) = 0
dy/y = ε₁ + ε₂ − ε₃

Q6: A variable w is related to three other variables x, y, z as w = xy/z. The variables are measured with meters of accuracy ±0.5% reading,  ±1% of full scale value and ±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 (2006)
(a) ±0.5% rdg
(b) ±5.5% rdg
(c) ±6.7% rdg
(d) ±7.0% rdg
Ans: (d)
Sol: Full scale reading of all three = 100
Reading of x = 80
Reading of y = 20
Reading of z = 50
δx = ±0.5% of reading
δy = ±1% of reading
δz = ±1.5% of reading
Given ω = xy/z
taking log, we get,
log⁡ω = log⁡x + log⁡y − log⁡z
differenting w.r.t. ω we get  
For maximum limiting error,

Q7: Resistances R₁ and R₂ have, respectively, nominal values of 10Ω and 5Ω, and tolerances of ±5 % and ±10%. The range of values for the parallel combination of R₁ and R₂ is  (2001)
(a) 3.077 Ω to 3.636 Ω
(b) 2.805 Ω to 3.371 Ω
(c) 3.237 Ω to 3.678 Ω
(d) 3.192 Ω to 3.435 Ω
Ans: (a)
Sol: Range of R₁ = 10 ± 10 × (5/100)
= 9.5Ω to 10.5Ω
Range of R₂ = 5 ± 5 × (10/100)
= 4.5Ω to 5.5Ω
= 3.05Ω to 3.61Ω