# NTA NET Electrical Engineering GATE 2018 Higher Questions and Answers Part 4

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**(Topic: Electromagnetic Fields)**

**(Subtopic:** **Capacitance of simple configurations)**

**(Sub-Subtopic:** **Capacitance of parallel plate capacitor)**

The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

**(Topic: Control Systems)**

**(Subtopic:** **Transient and Steady‐state analysis of linear time invariant systems)**

**(Sub-Subtopic:** **Final value theorem)**

The unit step response y(t) of a unity feedback system with open loop transfer function >

is shown in the figure. The value of K is _______ (up to 2 decimal places).

**(Topic: Electric Circuits)**

**(Subtopic:** **Three phase circuits)**

**(Sub-Subtopic:** **KCL)**

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If , and (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).

**(Topic: Electric Circuits)**

**(Subtopic:** **Power and power factor in AC circuits)**

**(Sub-Subtopic:** **Average power)**

The voltage across the circuit in the figure, and the current through it, are given by the following expressions:

𝑣(𝑡) = 5 − 10 cos(𝜔𝑡 + 60°) V

𝑖(𝑡) = 5 + 𝑋 cos(𝜔𝑡) A

where 𝜔 = 100 𝜋 radian/s. If the average power delivered to the circuit is zero, then the value of 𝑋 (in Ampere) is _____ (up to 2 decimal places).

**(Topic: Electric Circuits)**

**(Subtopic:** **Sinusoidal steady‐state analysis)**

**(Sub-Subtopic:** **Resonance)**

The voltage 𝑣(𝑡) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency 𝜔 = 100 radian/s. When the inductor current 𝑖(𝑡) is in phase with the voltage 𝑣(𝑡), the magnitude of the impedance Z (in Ω) seen between the terminals a and b is ________ (up to 2 decimal places).