List of practice Questions

The output impedance of a non-ideal operational amplifier is denoted by \( Z_{out} \). The variation in the magnitude of \( Z_{out} \) with increasing frequency, \( f \), in the circuit shown below, is best represented by:

An LTI system is shown in the figure where \[ G(s) = \frac{100}{s^2 + 0.1s + 10} \] The steady state output of the system, to the input \( r(t) \), is given as \[ y(t) = a + b \sin(10t + \theta) \] The values of 'a' and 'b' will be

The open loop transfer function of a unity gain negative feedback system is given as \[ G(s) = \frac{1}{s(s+1)}. \] The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point \( (-1 + j0) \) by the Nyquist plot of \( G(s) \), corresponding to the Nyquist contour, is denoted as \( N \). Then \( N \) equals to

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as \( \zeta \) and \( \omega_n \), respectively. The values of \( \zeta \) and \( \omega_n \) are

e\(^A\) denotes the exponential of a square matrix A. Suppose \( \lambda \) is an eigenvalue and \( \mathbf{v} \) is the corresponding eigen-vector of matrix A. Consider the following two statements: Statement 1: e\(^\lambda\) is an eigenvalue of e\(^A\). Statement 2: \( \mathbf{v} \) is an eigen-vector of e\(^A\). Which one of the following options is correct?

For the circuit shown below with ideal diodes, the output will be

A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ________ counter. (in integer)

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________. (round off to nearest integer)

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is _________. (round off to nearest integer)

The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is _________. (round off to one decimal place)

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ________. (round off to nearest integer)

In the circuit shown below, the switch S is closed at \( t = 0 \). The magnitude of the steady state voltage, in volts, across the 6 Ω resistor is ________. (round off to two decimal places)

A single-phase full-bridge diode rectifier feeds a resistive load of 50 \(\Omega\) from a 200 V, 50 Hz single-phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is _________. (round off to nearest integer)

The open loop transfer function of a unity gain negative feedback system is given by \[ G(s) = \frac{k}{s^2 + 4s - 5}. \text{ The range of } k \text{ for which the system is stable, is} \]

Consider a 3 x 3 matrix A whose \( (i, j) \)-th element, \( a_{i,j} = (i - j)^3 \). Then the matrix A will be

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100\(\sqrt{3}\) V with phase sequence ABC. The star connected load has \( Z_A = 10 \, \Omega \) and \( Z_B = 20 \angle 60^\circ \, \Omega \). The value of \( Z_C \) in \( \Omega \), for which the voltage difference across the nodes \( n \) and \( n' \) is zero, is

A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is \( J = J_a r^3 \hat{z} \) for the region \( r<b \) where \( r \) is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for \( r<b \)) is

The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

The transfer function of a real system, \( H(s) \), is given as:
\[ H(s) = \frac{As + B}{s^2 + Cs + D} \] where \( A \), \( B \), \( C \), and \( D \) are positive constants. This system cannot operate as:

For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is

The most commonly used relay, for the protection of an alternator against loss of excitation, is

The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

The steady state output \( V_{\text{out}} \), of the circuit shown below, will