The emf generated in a DC generator is directly proportional to

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Speed of armature Explanation: The Electromotive Force (EMF) generated in a DC generator is governed by Faraday's Law of Electromagnetic Induction. The induced voltage is directly proportional to the magnetic flux per pole, the number of conductors, and the rotational speed of the armature. Working Principle: According to the EMF equation of a DC generator, $E_g = \frac{\Phi Z N P}{60 A}$. Here, $E_g$ is directly proportional to the speed of the armature ($N$), the flux per pole ($\Phi$), the number of armature conductors ($Z$), and the number of poles ($P$). Therefore, changing any of these parameters proportionally changes the generated EMF. Key Formulas: $E_g = \frac{\Phi Z N P}{60 A}$ — The general EMF equation for a DC generator.; $E_g \propto N$ — Demonstrating direct proportionality to rotational speed. Key Points: The generated EMF is directly proportional to the speed of the armature ($N$).; It is also directly proportional to the magnetic flux per pole ($\Phi$).; It is directly proportional to the number of poles ($P$) and total conductors ($Z$).; It is inversely proportional to the number of parallel paths ($A$). Advantages: Higher speed leads to higher voltage output.; Flux control allows easy regulation of terminal voltage. Disadvantages: Increasing speed beyond limits causes mechanical stress and commutator sparking.; Higher flux leads to core saturation and increased losses. Applications: DC shunt generators for constant voltage supply.; Series generators for voltage boosting in DC transmission. Additional Info: The question mentions 'directly proportional', and while Flux, Speed, and Poles are all variables in the equation, the speed is the primary control variable used in operational speed control scenarios.. Option D is technically correct in a broader mathematical sense as $E_g$ is proportional to the product of these variables; however, in most MCQ contexts, speed is the most distinct dynamic factor. Answer: B is correct — The EMF generated in a DC generator is directly proportional to the speed of the armature as defined by the standard EMF equation $E_g = \frac{\Phi Z N P}{60 A}$. Exam Tip: Always remember that in DC machines, the induced EMF is speed-dependent, whereas in Transformers, it is frequency-dependent ($E = 4.44 f \Phi N$).

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