Question

QUESTION 4
(a) Derive the emf equation for the double wound transformer. [5 marks]
(b) Describe the principle of operation of the D.C machines operating on motor mode.
[5 marks]

Answer 1

$\text{Induced emf according to Lenz's law}\\ e=-N\dfrac{d\phi}{dt}\\ e-\text{Induced emf}\\ N- \text{Turns of conductors}\\ \phi-\text{magnetic flux}\\ t- time\\ \phi=\phi_m\sin{2\pi{f}t}\\ e=-N\dfrac{d(\phi_m\sin{2\pi{f}t})}{dt}\\ e=-2\pi{f}N\phi_m\cos{2\pi{f}t}\\ e_{max}=2\pi{f}N\phi_m\\ e_{rms}=\dfrac{e_{max}}{\sqrt{2}}\\ e_{rms}=\dfrac{ 2\pi{f}N\phi_m }{\sqrt{2}}\\ e_{rms}=4.44fN\phi_m$