List of top Electrical and Electronic Measurements Questions asked in GATE EE

The maximum percentage error in the equivalent resistance of two parallel connected resistors of 100 \( \Omega \) and 900 \( \Omega \), with each having a maximum 5% error, is: \[ {(round off to nearest integer value).} \]

The induced emf in a 3.3 kV, 4-pole, 3-phase star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no-load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of \( 2^\circ \) mechanical with respect to the terminal voltage phasor. If the synchronous reactance is \( 2 \, \Omega \), and stator resistance is negligible, then the motor armature current magnitude, in amperes, during loaded condition is closest to: \[ {(round off to two decimal places).} \]

In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage \( E \) for unit change in the resistance \( R \), in mV/\(\Omega\), is _____________ (round off to two decimal places).

An ideal low pass filter has frequency response given by
\[ H(j\omega) = \begin{cases} 1, & |\omega| \leq 200\pi \\ 0, & \text{otherwise} \end{cases} \] Let \( h(t) \) be its time domain representation. Then \( h(0) = \underline{\hspace{2cm}} \) (round off to the nearest integer). 

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be corrected to 0.85 pf lag. The line current of the capacitor bank, in A, is _____________ (round off to one decimal place). 

An ideal sinusoidal voltage source \( v(t) = 230\sqrt{2} \sin(2\pi \times 50t) \, \text{V} \) feeds an ideal inductor \( L \) through an ideal SCR with firing angle \( \alpha = 0^\circ \). If \( L = 100 \, \text{mH} \), then the peak of the inductor current, in ampere, is closest to:

An air filled cylindrical capacitor (capacitance \( C_0 \)) of length \( L \), with \( a \) and \( b \) as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity \( \varepsilon_r \) is inserted inside 50% of the annular region as shown in Fig. (ii). The value of \( \varepsilon_r \) for which the capacitance of the capacitor in Fig. (ii), becomes \( 5C_0 \) is 

The bus impedance matrix of a 3-bus system (in pu) is: \[ Z_{{bus}} = \begin{bmatrix} j0.059 & j0.061 & j0.038
j0.061 & j0.093 & j0.066
j0.038 & j0.066 & j0.110 \end{bmatrix} \] A symmetrical fault (through a fault impedance of \( j0.007 \) pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1 during the fault is: \[ {(round off to three decimal places).} \]
Consider two coupled circuits, having self-inductances \( L_1 \) and \( L_2 \), that carry non-zero currents \( I_1 \) and \( I_2 \), respectively. The mutual inductance between the circuits is \( M \) with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of \( \frac{I_1}{I_2} \)?
Instrument(s) required to synchronize an alternator to the grid is/are:

The operating region of the developed torque \( T_{em} \) and speed \( \omega \) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque \( T_L \) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time? 

Which one of the following figures represents the radial electric field distribution ER caused by a spherical cloud of electrons with a volume charge density,

ρ = -3ρ0 for 0 ≤ R ≤ a (both ρ0, a are positive and R is the radial distance),

and ρ = 0 for R > a?

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in \( \Omega \), that must be connected in series with the armature to reduce the speed of the motor by half, is closest to:
The 3-phase modulating waveforms \( v_a(t), v_b(t), v_c(t) \), used in sinusoidal PWM in a Voltage Source Inverter (VSI) are given as: \[ v_a(t) = 0.8 \sin(\omega t) \quad v_b(t) = 0.8 \sin\left(\omega t - \frac{2\pi}{3}\right) \quad v_c(t) = 0.8 \sin\left(\omega t + \frac{2\pi}{3}\right) \] where \( \omega = 2\pi \times 40 \, {rad/s} \) is the fundamental frequency. The modulating waveforms are compared with a 10 kHz triangular carrier whose magnitude varies between +1 and -1. The VSI has a DC link voltage of 600 V and feeds a star connected motor. The per phase fundamental RMS motor voltage, in volts, is closest to:

In the circuit, \( I_{\text{DC}} \) is an ideal current source, the transistors \( M_1 \), \( M_2 \) are assumed to be biased in saturation wherein \( V_{\text{in}} \) is the input signal and \( V_{\text{DC}} \) is the fixed DC voltage. Both transistors have a small signal resistance of \( R_{ds} \) and transconductance of \( g_m \). The small signal output impedance of the circuit is:
 

The open-loop transfer function of the system shown in the figure is: \[ G(s) = \frac{K s (s + 2)}{(s + 5)(s + 7)} \] For \( K \geq 0 \), which of the following real-axis points is on the root locus?
A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as the cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume a linear magnetic circuit. The external resistance in ohms that must be connected in series with the armature to reduce the speed of the motor by half is closest to:
Instruments required to synchronize an alternator to the grid are:
The induced EMF in a 3.3 kV, 4-pole, 3-phase, Y-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no-load condition. On application of a mechanical load, the induced EMF phasor is deflected by an angle of 2 degrees with respect to the terminal voltage phasor. If the isochronous reactance is 2 ohms and the series resistance is negligible, the motor armature current magnitude, in amperes, during loaded condition, is closest to:

The maximum percentage error in the equivalent resistance of two parallel connected resistors of 100 ohm and 900 ohm, with each having a maximum 5% error, is:

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be improved to 0.85 pf lag. The line current of the capacitor bank in amperes, which is connected in parallel to the load is:

The op-amps in the following circuit are ideal. The voltage gain of the circuit is ……….. . (Round off to the nearest integer) 
 

The maximum percentage error in the equivalent resistance of two parallel connected resistors of 100 \( \Omega \) and 900 \( \Omega \), with each having a maximum 5% error, is: \[ \text{(round off to nearest integer value).} \]
The induced emf in a 3.3 kV, 4-pole, 3-phase star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no-load condition.

On application of a mechanical load, the induced emf phasor is deflected by an angle of \( 2^\circ \) mechanical with respect to the terminal voltage phasor.
If the synchronous reactance is \( 2 \, \Omega \), and stator resistance is negligible, then the motor armature current magnitude, in amperes, during loaded condition is closest to: \[ \text{(round off to two decimal places).} \]

In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage \( E \) for unit change in the resistance \( R \), in V/Ω, is __________ (round off to two decimal places).