List of top Questions asked in GATE IN

For the full bridge made of linear strain gauges with gage factor 2 as shown in the diagram, \( R_1 = R_2 = R_3 = R_4 = 100 \, \Omega \) at 0°C and strain is 0. The temperature coefficient of resistance of the strain gauges used is 0.005 per °C. All strain gauges are made of the same material and exposed to the same temperature. While measuring a strain of 0.01 at a temperature of 50°C, the output \( V_o \) in millivolt is \(\underline{\hspace{1cm}}\) (rounded off to two decimal places). 
 

In the bridge circuit shown, the voltmeter \( V \) showed zero when the value of the resistors are: \( R_1 = 100 \, \Omega \), \( R_2 = 110 \, \Omega \), and \( R_3 = 90 \, \Omega \). If \( \frac{R_1}{R_2} = \frac{R_A}{R_B} \), the value of \( R_4 \) in ohm is \(\underline{\hspace{2cm}}\). 

A 3½ digit, rectifier type digital meter is set to read in its 2000 V range. A symmetrical square wave of frequency 50 Hz and amplitude \( \pm 100 \) V is measured using the meter. The meter will read \(\underline{\hspace{2cm}}\). 
 

The power in a 400 V (rms, line-line) three-phase, three-wire RYB sequence system is measured using the two wattmeters, as shown. The R-line current is \( 5 \angle 60^\circ \, \text{A} \). Wattmeter \( W_1 \) in the R-line will read (in watts) \(\underline{\hspace{2cm}}\). 

The circuit shown below uses an ideal OpAmp. Output \( V_o \) in volt is \(\underline{\hspace{2cm}}\) (rounded off to one decimal place). 

All the transistors used in the circuit are matched and have a current gain \( \beta = 20 \). Neglecting the Early effect, the current \( I_{O4} \) in milliamperes is \(\underline{\hspace{2cm}}\). 

A bar primary current transformer of rating 1000/1 A, 5 VA, UPF has 995 secondary turns. It exhibits zero ratio error and phase error of 30 minutes at 1000 A with rated burden. The watt loss component of the primary excitation current in amperes is \(\underline{\hspace{2cm}}\) (rounded off to one decimal place).
A signal having a bandwidth of 5 MHz is transmitted using the Pulse Code Modulation (PCM) scheme as follows. The signal is sampled at a rate of 50% above the Nyquist rate and quantized into 256 levels. The binary pulse rate of the PCM signal in Mbits per second is \(\underline{\hspace{1cm}}\).
An air-cored coil having a winding resistance of 10 \(\Omega\) is connected in series with a variable capacitor \( C_x \). The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin effect, the value of the inductance of the coil in millihenry is \(\underline{\hspace{2cm}}\).
A household fan consumes 60 W and draws a current of 0.3125 A (rms) when connected to a 230 V (rms) ac, 50 Hz single-phase mains. The reactive power drawn by the fan in VAr is \(\underline{\hspace{2cm}}\) (rounded off to the nearest integer).
Consider that \( X \) and \( Y \) are independent continuous valued random variables with uniform PDF given by \( X \sim U(2, 3) \) and \( Y \sim U(1, 4) \). Then \( P(Y \leq X) \) is equal to \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).
A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \) and \( \mu_r \) of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is \(\underline{\hspace{2cm}}\).
A 10½ digit Counter-timer is set in the 'frequency mode' of operation (with \( T_s = 1 \, \text{s} \)). For a specific input, the reading obtained is 1000. Without disconnecting this input, the Counter-timer is changed to operate in the 'Period mode' and the range selected is microseconds (\( \mu s \), with \( f_s = 1 \, \text{MHz} \)). The counter will then display
The function \[ f(z) = (z - 1)^{-1} - 1 + (z - 1) - (z - 1)^2 + \cdots \] is the series expansion of
A single-phase transformer has maximum efficiency of 98%. The core losses are 80 W and the equivalent winding resistance as seen from the primary side is 0.5 \( \Omega \). The rated current on the primary side is 25 A. The percentage of the rated input current at which the maximum efficiency occurs is
A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is
A piezoresistive pressure sensor has a sensitivity of 1 (mV/V)/kPa. The sensor is excited with a dc supply of 10 V and the output is read using a 3 ½ digit 200 mV full-scale digital multimeter. The resolution of the measurement set-up, in pascal is \(\underline{\hspace{2cm}}\).
An amplitude modulation (AM) scheme uses tone modulation, with modulation index of 0.6. The power efficiency of the AM scheme is \(\underline{\hspace{2cm}}\) % (rounded off to one decimal place).
When the movable arm of a Michelson interferometer in vacuum \( (n = 1) \) is moved by 325 \(\mu m\), the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is \(\underline{\hspace{2cm}}\).
Consider the function \( f(x) = -x^2 + 10x + 100 \). The minimum value of the function in the interval \( [5, 10] \) is \(\underline{\hspace{2cm}}\).
A 300 V, 5 A, LPF wattmeter has a full scale of 300 W. The wattmeter can be used for loads supplied by 300 V ac mains with a maximum power factor of \(\underline{\hspace{2cm}}\) (rounded off to one decimal place).
A 10-bit ADC has a full-scale of 10.230 V, when the digital output is \( (11 \, 1111 \, 1111)_2 \). The quantization error of the ADC in millivolt is \(\underline{\hspace{2cm}}\).
A strain gage having nominal resistance of 1000 \( \Omega \) has a gage factor of 2.5. If the strain applied to the gage is 100 \( \mu \)m/m, its resistance in ohm will change to \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).
Given: Density of mercury is 13,600 kg/m\(^3\) and acceleration due to gravity is 9.81 m/s\(^2\). Atmospheric pressure is 101 kPa. In a mercury U-tube manometer, the difference between the heights of the liquid in the U-tube is 1 cm. The differential pressure being measured in pascal is \(\underline{\hspace{2cm}}\) (rounded off to the nearest integer).
A single-phase transformer has a magnetizing inductance of 250 mH and a core loss resistance of 300 \(\Omega\), referred to primary side. When excited with a 230 V, 50 Hz sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).