UPSC ESE Electrical Engineering Solved Papers

What is the DC gain (zero frequency) for a system which has a transfer function of $$G(s)=(s+2)/((s+1)(s+3)(s+4))$$?

Match the following Lists:

Select the correct answer using the code given below:

Consider the following steps regarding multiple-node electrical networks:

1. Replace passive elements' values with their admittance variables
2. Replace all sources and time variables with their Laplace transform
3. Replace transformed voltage sources with transformed current sources

Which of the above steps are correct?

What is the transfer function T(s) from the state-space input matrix $$\dot{x}=[A]x+[B]u$$ and output matrix $$y=[C]x$$, where $$T(s)=Y(s)/U(s)$$, while $$U(s)$$ is input and $$Y(s)$$ is output?

$$\dot{x}=\begin{bmatrix}0 & 1 & 1 \\ 0 & 0 & 1 \\ -1 & -2 & -3\end{bmatrix}x+\begin{bmatrix}10 \\ 0 \\ 0\end{bmatrix}u; \quad y=\begin{bmatrix}1 & 0 & 0\end{bmatrix}x$$

Consider the following statements regarding first-order systems:

1. The time constant of the system can be described as the time for $$e^{-\alpha t}$$ to decay to 63% of initial value or it is the time taken for the step response to rise to 37% of its final value.
2. Rise time is found to be the time for waveform to go from 0-1 to 0-9 of its final value.
3. Settling time is defined as the time for the response to reach and stay within 4% of its final value.

Which of the above statements is/are not correct?

Consider the following statements regarding behavior of second-order underdamped system:

1. The peak time is inversely proportional to the imaginary part of the complex pole.
2. Percent overload is a function of only the damping ratio.
3. Settling time is directly proportional to the real part of the complex pole.

Which of the above statements are correct?

For the closed-loop transfer function given below, what is the system condition based on the number of poles in the left-half plane, the right-half plane and the $$j\omega$$-axis?

$$T(s)=\frac{200}{s^4+6s^3+11s^2+6s+200}$$

Consider the following statements regarding stability for linear, time-invariant systems using natural response:

1. A system is marginally stable, if the natural response neither decays nor grows but remains constant or oscillates.
2. A system is unstable, if the natural response approaches infinity as time approaches zero.
3. A system is unstable, if any bounded input yields an unbounded output.

Which of the above statements is/are not correct?

What are the values of positive constant $$(K_p)$$, velocity constant $$(K_v)$$ and acceleration constant $$(K_a)$$ for a type '0' unity feedback system which has the transfer function $$G(s)=\frac{1000(s+8)}{(s+7)(s+9)}$$?

Consider the following statements regarding properties of a transfer function:

1. The unit of a transfer function is related to the units of the system input and output. A unit is essential.
2. The transfer function can be applied to describe only time-invariant linear systems whose parameters do not change or change only a little during operation.
3. The transfer function is dependent of the input to the system, since the characteristics of the system are modified by the input signal.

Which of the above statements is/are correct?

Consider the following and give the order of the steps to be followed in performing the block diagram reduction to get the final transfer function for that system:

Step 1: Combine all serial blocks
Step 2: Close all inner loops
Step 3: Combine all parallel blocks
Step 4: Move summing junctions to the left or right of a block and tie points to the left or right

Select the correct sequence for the above steps.

Consider the following statements regarding representation of block diagrams through signal flow diagrams:

1. The signal at a node is equal to the sum of all signals transmitted to the node. Sometimes, the transmittance may be positive.
2. The transmittances are simply related to the transfer functions.
3. The transmittances connected to the input/output nodes are both unity; and merely help to make the diagram clearer.

Which of the above statements is/are correct?

Consider the following statements regarding Nyquist stability criterion:

1. The Nyquist stability criterion is one of the geometric criterion and graphical method in frequency domain.
2. It uses open-loop Nyquist diagram to judge the stability of the closed-loop system.
3. Instead of solving the characteristic roots of the open-loop system, the Nyquist criterion gets the stability of the closed-loop system by means of an open-loop frequency characteristic diagram.

Which of the above statements are correct?

A transformer on no-load has a core loss of 50 W, draws a current of 2 A (rms) and has an induced emf of 230 V (rms). What is the core loss current?

A 500 kVA transformer has an efficiency of 95% at full load and also at 60% of full load; both at unity power factor. Separate out the losses of the transformer.

Consider the following statements regarding three-phase transformer connections:

1. Delta/delta is economical for small HV transformers.
2. Star/star suits large LV transformers.
3. Star/delta is the most commonly used connection for power systems.

Which of the above statements is/are correct?

A 240 V/120 V, 12 kVA transformer has full-load unity power factor efficiency of 96-2%. It is connected as an auto-transformer to feed a load at 360 V. What is the auto-transformer rating?

The magnetic flux density on the surface of an iron face is 1.6 T, which is a typical saturation level value for ferromagnetic material. What is the force density on the iron face?

For a 6-pole DC armature with 16 slots having two coil sides per slot and single-turn coils, what is the commutator pitch ($y_c$) for a wave winding?

Consider the following statements regarding speed control of DC motors:

1. In field control method, speeds higher than the rated speed cannot be obtained.
2. For motors requiring a wide range of speed control, field control method leads to unstable operating conditions or poor commutation.
3. Field control method is not suited to applications needing speed reversal.

Which of the above statements is/are correct?

Which one of the following is not the remedy for reducing cross-magnetizing effect of the armature reaction?

The total iron losses in the armature of a DC machine running at 875 rpm are 1100 W. What is the approximate braking torque due to iron losses?

A 0-5 hp, 6-pole induction motor is excited by a 3-phase, 60 Hz source. If the full-load speed is 1140 rpm, what is the percentage of slip?

A 50 Hz induction motor wound for pole-amplitude modulation has 20 initial poles and the modulating function has 8 poles. At what two speeds will the motor run?

A 3-phase synchronous generator produces an open-circuit line voltage of 6928 V, when the DC exciting current is 50 A. The AC terminals are then short-circuited and the three line currents are found to be 800 A. What is the synchronous reactance per phase?