Question 1 |

Consider g(t)=\left\{\begin{matrix} t-\left \lceil t \right \rceil, & t\geq 0 \\ t-\left \lceil t \right \rceil , & otherwise \end{matrix}\right. , \; \; where\; t \in \mathbb{R}

Here, \left \lfloor t \right \rfloor represents the largest integer less than or equal to t and \left \lceil t \right \rceil denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

Here, \left \lfloor t \right \rfloor represents the largest integer less than or equal to t and \left \lceil t \right \rceil denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

0 | |

1 | |

2 | |

3 |

Question 1 Explanation:

Given that, g(t)=\left\{\begin{matrix} t-\left \lfloor t \right \rfloor, & t \geq 0\\ t-\left \lceil t \right \rceil & \text{otherwise} \end{matrix}\right.

where,

\left \lfloor t \right \rfloor= greatest integer less than or equal to 't'.

\left \lceil t \right \rceil= smallest integer greater than or equal to 't'.

Now,

Since, g(t) is nonperiodic. So, there is no Fourier series expansion of this signal and hence no need to calculate harmonic here.

where,

\left \lfloor t \right \rfloor= greatest integer less than or equal to 't'.

\left \lceil t \right \rceil= smallest integer greater than or equal to 't'.

Now,

Since, g(t) is nonperiodic. So, there is no Fourier series expansion of this signal and hence no need to calculate harmonic here.

Question 2 |

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure
below. The instantaneous voltage and current in phase-a are V_{an}=220sin(100\pi t)V and i_{a}=10sin (100\pi t)A, respectively. Similarly for phase-b the instantaneous voltage and current are V_{bn}=220cos (100\pi t)V and i_{b}=10cos( 100\pi tA, respectively

The total instantaneous power flowing form the source to the load is

The total instantaneous power flowing form the source to the load is

2200W | |

2200 sin^{2}(100\pi t)W | |

440W | |

2200 sin(100\pi t) cos(100 \pi t) W |

Question 2 Explanation:

\begin{aligned} V_{an}&=220 \sin (100 \pi t)V\\ i_a&=10 \sin (100 \pi t)A\\ V_{bn}&=220 \cos (100 \pi t)V\\ i_b&=10 \cos (100 \pi t)A\\ p&=V_{an}i_a+V_{bn}i_b\\ &=2200 W \end{aligned}

Question 3 |

A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a
motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor
(UPF). The synchronous reactance of the motor is 30 \Omega per phase. The load angle is 30^{\circ}. The power delivered to the motor in kW is _______.

2520.5 | |

1640.8 | |

838.3 | |

400.8 |

Question 3 Explanation:

For synchronous motor,

\bar{V_t}=\bar{E_f}+j\bar{I_a}X_s

As currrent is drawn at unity power factors.

Therefore,

\begin{aligned} E_f \cos \delta &=V_t \\ E_f&= \frac{V_t}{\cos \delta }=\frac{6.6kV}{\sqrt{3}} \times \frac{1}{\cos 30^{\circ}}\\ E_f&= \frac{6.6 \times 10^3}{\sqrt{3} \times \sqrt{3}} \times 2V\\ V_t &=\frac{6.6 \times 10^3}{\sqrt{3}} \\ \therefore \;\;P_e &=\frac{3V_{ph}E_{ph}}{X_s} \sin \delta \\ &= \frac{3 \times \frac{6.6 \times 10^3}{\sqrt{3}} \times \frac{6.6 \times 10^3}{\sqrt{3} \times \sqrt{3}} \times 2 }{30} \times \sin 30^{\circ}\\ &=838.3kW \end{aligned}

\bar{V_t}=\bar{E_f}+j\bar{I_a}X_s

As currrent is drawn at unity power factors.

Therefore,

\begin{aligned} E_f \cos \delta &=V_t \\ E_f&= \frac{V_t}{\cos \delta }=\frac{6.6kV}{\sqrt{3}} \times \frac{1}{\cos 30^{\circ}}\\ E_f&= \frac{6.6 \times 10^3}{\sqrt{3} \times \sqrt{3}} \times 2V\\ V_t &=\frac{6.6 \times 10^3}{\sqrt{3}} \\ \therefore \;\;P_e &=\frac{3V_{ph}E_{ph}}{X_s} \sin \delta \\ &= \frac{3 \times \frac{6.6 \times 10^3}{\sqrt{3}} \times \frac{6.6 \times 10^3}{\sqrt{3} \times \sqrt{3}} \times 2 }{30} \times \sin 30^{\circ}\\ &=838.3kW \end{aligned}

Question 4 |

For a complex number z, \lim_{z\rightarrow i}\frac{z^{2}+1}{z^{3}+2z-i(z^{2}+2)} is

-2i | |

-i | |

i | |

2i |

Question 4 Explanation:

\begin{aligned} \lim_{z \to i}&=\frac{z^2+1}{z^3+2z-i(z^2+2)}\\ \lim_{z \to i}&=\frac{2z}{3z^2+2-i(2z)}\\ &=\frac{2i}{3i^2+2-i(2i)}\\ &=\frac{2i}{-3+2+2}\\ &=\frac{2i}{-3+4}=2i \end{aligned}

Question 5 |

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such
that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the
particles are released but are constrained to move along the same straight line. Which of these
will collide first?

The particles will never collide | |

All will collide together | |

Proton and Neutron | |

Electron and Neutron |

Question 5 Explanation:

Given that electron, neutron and proton are in straight line.

The electron will move towards proton and proton will move towards electron and force will be same F=\frac{q_1q_2}{4 \pi \in _0 R^2}. But acceleration of electron will be more than proton as mass of electron \lt mass of proton. Since neutron are neutral they will not move. Thus electron will hit neutron first.

The electron will move towards proton and proton will move towards electron and force will be same F=\frac{q_1q_2}{4 \pi \in _0 R^2}. But acceleration of electron will be more than proton as mass of electron \lt mass of proton. Since neutron are neutral they will not move. Thus electron will hit neutron first.

There are 5 questions to complete.