# Electrical and Electronic Measurements

 Question 1
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 1 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 2
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 2 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 3
Inductance is measured by
 A Schering bridge B Maxwell bridge C Kelvin bridge D Wien bridge
GATE EE 2021      A.C. Bridges
Question 3 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 4
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
 Question 5
Currents through ammeters A2 and A3 in the figure are $1\angle 10^{\circ} \; and \; 1\angle 70^{\circ}$ respectively. The reading of the ammeter A1 (rounded off to 3 decimal places) is ________ A.
 A 1.121 B 1.732 C 2.254 D 3.214
GATE EE 2020      Galvanometers, Voltmeters and Ammeters
Question 5 Explanation:
$I=1\angle 10^{\circ}+1\angle 70^{\circ}$
$I=1.732\angle 40^{\circ}$
The ready of ammeter is 1.732 A.
 Question 6
The voltage across and the current through a load are expressed as follows
$v(t)=-170sin(377t-\frac{\pi}{6})V$
$i(t)=8 cos(377t+\frac{\pi}{6})A$
The average power in watts (round off to one decimal place) consumed by the load is _______.
 A 340.5 B 170.6 C 588.9 D 377.8
GATE EE 2019      Measurement of Energy and Power
Question 6 Explanation:
\begin{aligned} v(t) &=-170 \sin \left ( 377t-\frac{\pi}{6} \right )V=V_{pc}\\ i(t) &= 8 \cos \left ( 377t+\frac{\pi}{6} \right )A=I_{cc}\\ i(t) &= 8 \sin \left ( 377t+\frac{2\pi}{3} \right )A=I_{cc} \\ P_{avg}&=\frac{1}{2} \times (-170)(8) \times \cos\left ( -\frac{\pi}{6}-\frac{2 \pi}{3} \right ) \\ &= \frac{1}{2} \times (-170)(8) \times \cos(150^{\circ}) \\ &=588.9W \end{aligned}
 Question 7
A moving coil instrument having a resistance of 10 $\Omega$, gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V?
 A 9$\Omega$ B 99$\Omega$ C 990$\Omega$ D 9990$\Omega$
GATE EE 2019      Galvanometers, Voltmeters and Ammeters
Question 7 Explanation:

\begin{aligned} V_m&=I_mR_m \\ &= 10 mA \times 10\Omega \\ &= 100mV\\ (0-100mV)\Rightarrow & (0-100V)\\ m &= \frac{V_{ext}}{V_m}=\frac{100V}{100mV}=1000\\ R_{se}&=R_m[m-1] \\ R_{se} &= 10(1000-1)\\ &= 9990\Omega \end{aligned}
 Question 8
A 0-1 Ampere moving iron ammeter has an internal resistance of 50 m$\Omega$ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in m$\Omega$ of the shunt coil respectively are
 A 2, 5.55 B 2, 1 C 2.18, 0.55 D 11.1, 2
GATE EE 2018      Galvanometers, Voltmeters and Ammeters
Question 8 Explanation:
Given,
$I_m=1A,$
$R_m=50m\Omega$
$L_m=0.1 mH,$
$I=10A$
We know,
$R_{sh}=\frac{R_m}{(m-1)};$
$m=\frac{I}{I_m}=\frac{10}{1}=10$
$R_{sh}=\frac{50 \times 10^{-3}}{10-1}$
$\;\;=5.55m\Omega$
For all frequencies time constant of shunt and meter arm should be equal.
\begin{aligned} i.e. \;\; \frac{\omega L_m}{R_m} &=\frac{\omega L_{sh}}{R_{sh}} \\ \frac{L_m}{R_m} &= \frac{L_{sh}}{R_{sh}}\\ \frac{L_m}{R_m} &= \frac{0.1 \times 10^{-3}}{50 \times 10^{-3}}\\ &=0.002=2ms \end{aligned}
 Question 9
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is
 A 0.532 B 0.632 C 0.707 D 0.866
GATE EE 2018      Measurement of Energy and Power
Question 9 Explanation:
In two wattmeter method,
$\tan \phi =\frac{\sqrt{3}(W_1-W_2)}{W_1+W_2}$
\begin{aligned} \text{Given}, \; W_2 &=\frac{W_1}{2} \\ \tan \phi &=\frac{\sqrt{3}\left (W_1-\frac{W_1}{2} \right ) }{\left (W_1+\frac{W_1}{2} \right )} \\ \phi &= 30^{\circ}\\ \cos \phi &=\cos 30^{\circ}=0.866 \end{aligned}
 Question 10
A $10\frac{1}{2}$ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.
 A 100 B 1000 C 10000 D 100000
GATE EE 2017-SET-2      CRO and Electronic Measurements
Question 10 Explanation:
$1.\;\;10\frac{1}{2}$ digital time counter:
Frequency mode of operation: $f=\frac{n}{t}$

Let f = frequency of input signal
n = number of cycles of repetitive signal
$\Rightarrow \;\;100 \times 10^6$
Let $t \Rightarrow$ Gate time $\Rightarrow \;t=1 sec.$
$f=\frac{100 \times 10^6}{1 sec}=10^8 Hz$
$\;\;=10^8 cycles/sec$
On $10\frac{1}{2}$ digit display
$100000000.00Hz$

$2.\;\; \text{Period mode of operation:}$
$P=\frac{1}{f}=\frac{t}{n}=\frac{1sec}{100 \times 10^6}$
Let P=Period of input signal
$P=0.01 \times 10^{-6}$
$\;\;=10 \times 10^{-9}$
$\;\;=1 \times 10n-sec$
$\;\;=10.000000000 n-sec$

There are 10 questions to complete.