The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, R_{\text{thermisor }}=2(1+ aT) K Ω, where T is the temperature in { }^{\circ} {C}. The temperature coefficient, a, is -(4 \pm 0.25) \% {/}{ }^{\circ} {C}. Circuit parameters: {R}_{1}=1 {K} Ω, {R}_{2}=1.3 {k} Ω, {R}_{3}=2.6 {k} Ω. The error in the output signal (in {V}, rounded off to 2 decimal places) at 150^{\circ} {C} is__________

GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 61 of 65

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The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance,

R_{\;\text "thermisor "\;}=2(1+

aT)

K Ω

, where

T

is the temperature in

{ }^{∘} {C}

. The temperature coefficient,

a

, is

-(4 ± 0.25)

\% {/}{ }^{∘} {C}

. Circuit parameters:

{R}_{1}=1 {K} Ω, {R}_{2}=1.3 {k} Ω, {R}_{3}=2.6 {k} Ω

. The error in the output signal (in

{V}

, rounded off to 2 decimal places) at

150^{∘} {C}

is__________

Your Answer:

Validate

Solution:

Given

{Rr}=2(1+2 {T}) {k} Ω

\;\text " Case-i "\; {a}=-4 \%

R_{T}=2(1-\;{4 × 150}/{100})=-10 k Ω

{V}_{0}=3 × \;{1 {k} Ω}/{}

V_{0}=3 × \;{R_{1}}/{R_{1}+R_{T}}(1+\;{R_{3}}/{R_{2}})-0.1 × \;{R_{3}}/{R_{3}}

V_{0}=-1.2

Case-ii

R_{T}=2(1+2 T)

{a}=-3.75 \%

{R}_{ {T}}=-9.25

{V}_{0}=3 × \;{1}/{1-9.25}[3]-0.2

{V}_{0}=-1.290

Case-iii

a=4.25

R_{ {r}}=2(1+2 T)

R_{ {T}}=10.75

V_{0}=-1.12

=-1.2 ± 0.08

Error

=0.08

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