# Electrical and Electronic Measurements

 Question 1
A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400V (rms), balanced voltage source with phase sequence $R-Y-B$, as shown in the figure. If the wattmeter reading is $-400 \mathrm{~W}$ and the line current is $\mathrm{I}_{\mathrm{R}}=2 \mathrm{~A}(\mathrm{rms})$, then the power factor of the load per phase is

 A Unity B 0.5 leading C 0.866 leading D 0.707 lagging
GATE EE 2023      Measurement of Energy and Power
Question 1 Explanation:
By observation of wattmeter connection, the wattmeter read reactive power
$\because$ Wattmeter reading,
$W=Y_{Y B} I_{R}$ (Angle between $V_{Y B}$ and $I_{R}$.

Phasor diagram :

$\therefore \quad W=V_{\mathrm{L}} \mathrm{I}_{\mathrm{L}} \cos \left(90^{\circ}-\beta\right)$
$=V_{L} I_{L} \sin \phi$

Given: $\quad W=-400 \mathrm{~W}$
$\therefore \quad-400=400 \times 2 \times \sin \phi$
$\Rightarrow \quad \phi=-30^{\circ}$

Thus, P.F. $=\cos \phi=0.866$ leading
 Question 2
Two balanced three-phase loads, as shown in the figure, are connected to a $100\sqrt{3}V$, three-phase, 50 Hz main supply. Given $Z_1=(18+j24)\Omega$ and $Z_2=(6+j8)\Omega$. The ammeter reading, in amperes, is _______. (round off to nearest integer)

 A 15 B 20 C 18 D 22
GATE EE 2022      Galvanometers, Voltmeters and Ammeters
Question 2 Explanation:
First perform delta to star conversion we know, for balanced load
$Z_{star}=\frac{Z_{delta}}{3}=\frac{18+j24}{3}=6+j8\Omega$
Draw the per phase diagram:

$Z_{eq}=(6+j8)||(6+j8)=(3+j8)\Omega =5\angle 53.13^{\circ} \Omega$
Therefore, Meter reading, $I=\frac{100}{5}=20A$

 Question 3
A balanced Wheatstone bridge $ABCD$ has the following arm resistances:
$R_{AB}=1k\Omega \pm 2.1%; R_{BC}=100\Omega \pm 0.5%, R_{CD}$ is an unknown resistance; $R_{DA}=300\Omega \pm 0.4%;$. The value of $R_{CD}$ and its accuracy is
 A $30\Omega \pm 3\Omega$ B $30\Omega \pm 0.9\Omega$ C $3000\Omega \pm 90\Omega$ D $3000\Omega \pm 3\Omega$
GATE EE 2022      A.C. Bridges
Question 3 Explanation:
The condition for balanced bridge
\begin{aligned} R_{AB}R_{CD}&=R_{DA}R_{BC} \\ R_{CD} &=\frac{300 \times 100}{1000}=30\Omega \\ %Error &=\pm (2.1+0.5+0.4)=\pm 3% \\ \therefore \; R_{CD}&=30\pm 30 \times \frac{3}{100}=30\pm 0.9\Omega \end{aligned}
 Question 4
Inductance is measured by
 A Schering bridge B Maxwell bridge C Kelvin bridge D Wien bridge
GATE EE 2021      A.C. Bridges
Question 4 Explanation:
Maxwell's bridge is used for measurement of inductance.
Wein's bridge is used for measurement of frequency
Kelvin's bridge is used for measurement of low value of resistance.
Schering bridge is used for measurement of capacitance, dilectric loss and permittivity etc.
 Question 5
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 _______.
 A 5.87 B 2.35 C 11.5 D 9.2
GATE EE 2020      Characteristics of Instruments and Measurement Systems

There are 5 questions to complete.