GATE EE 2015 Set 1 — Question 31
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Electrical Machines → DC Machines → First-Order RL & RC
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Question
A separately excited DC generator has an armature resistance of and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is . When this generator is operated at half the rated speed, with half the rated field current, an uncharged capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach ?
Correct answer
(B) 69.3
Solution
1.The generated EMF of a DC generator is given by , where is the flux and is the speed.
2.Assuming a linear magnetic circuit, flux is proportional to field current: . Thus, .
3.At rated conditions: .
4.At half speed () and half field current ():
.5.When the capacitor is connected, the circuit is a simple RC charging circuit with , , and .
6.The voltage across the capacitor is .
7.Time constant .
8.Setting :
.
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