GATE 2023 IN Q.64: solution and answer

GATE 2023 · INQ.64 · 2 marks · NAT

A 1.999 V True RMS 3-1/2 digit multimeter has an accuracy of

$\pm 0.1 %$ of reading $\pm 2$ digits.

It is used to measure 100 A (RMS) current flowing through a line using a 100:5 ratio, Class-1 current transformer with a burden of $0.1 Ω \pm 0.5 %$ .

The worst-case absolute error in the multimeter output is ________ V (rounded off to three decimal places).

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Answer and solution

ANSWER

The worst-case absolute error in the multimeter output is $0.010 V$ .

Official answer: 0.009 to 0.011Source: Official answer key, GATE 2023 IN (IIT Kanpur)

CT secondary current (ratio 100:5): $I_{s} = 100 \times \frac{5}{100} = 5 A$ . The line current of $100 A$ is the CT's rated primary current, so the Class-1 limit applies in full.
The multimeter reads the voltage across the burden: $V = I_{s} R = 5 \times 0.1 = 0.5 V$ (nominal reading). This lies on the $1.999 V$ range.
A Class-1 CT has a ratio (current) error of up to $\pm 1 %$ at rated current, and the burden resistance is $\pm 0.5 %$ . Since $V = I_{s} R$ is a product, the limiting relative errors add: $\pm (1 + 0.5) = \pm 1.5 %$ .
Error in the voltage presented to the meter: $1.5 % \times 0.5 V = \pm 0.0075 V$ .
Meter reading error: $0.1 %$ of reading $= 0.001 \times 0.5 V = \pm 0.0005 V$ .
Digit error: on the $1.999 V$ range of a 3½-digit meter one count (the least significant digit) is $0.001 V$ , so $\pm 2$ digits $= \pm 0.002 V$ .
Worst case, all errors add in the same direction: $Δ V = 0.0075 + 0.0005 + 0.002 = 0.0100 V$ If you take $0.1 %$ of the worst-case reading $0.5075 V$ instead, you get $0.01001 V$ , which still rounds to $0.010 V$ .

KEY IDEA

The meter measures $V = I_{s} R$ across the CT burden. For the worst case, add the limiting relative errors of the CT ratio (Class 1, so $\pm 1 %$ ) and the burden ( $\pm 0.5 %$ ), turn that into volts at the $0.5 V$ reading, then add the meter's own error: $0.1 %$ of reading plus 2 counts of $0.001 V$ each on the $1.999 V$ range.

WATCH OUT FOR

The usual mistakes are leaving out the digit error or giving it the wrong size. On a 3½-digit meter, $\pm 2$ digits on the $1.999 V$ range is $\pm 0.002 V$ , and that alone is 20 % of the answer. Other slips: forgetting the burden tolerance, or combining the errors as a root-sum-square when the question asks for the worst case, which is a straight sum.

From the GATE 2023 IN paper. Every question of this paper · Download the full paper · All 2 Digital instruments questions, with notes