EE-100 Basics of Electrical Engineering DEC 2017

Q1: Explain the basic working principle of a transformer. Answer: A transformer is a static electrical device used to transfer electrical energy from one circuit to another at the same frequency but with different voltage and current levels. It works on the principle of mutual induction: when an alternating current flows through a primary coil wound on a magnetic core, it produces a time-varying magnetic flux. This flux links with the secondary coil, inducing an electromotive force (emf) in it. Faraday’s Law of Electromagnetic Induction: $$e= -N \frac{dϕ}{dt}$$ where 𝑁 = number of turns, Voltage ratio:$$\frac{V_{1}}{V_{2}} = \frac{N_{1}}{N_{2}} =k$$ 

where k = turns ratio.

 Step 5 (Ideal case current relation): ​​ $$\frac{I_{1}}{I_{2}} = \frac{N_{2}}{N_{1}}$$

Step 4 – Turns ratio relation:

$$\frac{E_{1}}{E_{2}} = \frac{N_{1}}{N_{2}} =k$$

 

Q: Explain the construction and working of an electrolytic capacitor with neat diagram. (5 marks)

Answer:

• Construction: Made of two aluminum foils (anode & cathode) separated by paper soaked in electrolyte. Anodized oxide layer (Al₂O₃) on anode acts as dielectric. Enclosed in can, polarity marked.

• Working: Positive voltage → oxide layer blocks DC → capacitor stores charge. Very thin dielectric ⇒ large capacitance. Reversing polarity destroys oxide.

• -------Equation:$$C = \dfrac{\varepsilon A}{d}$$

(Draw cross-sectional diagram of foil, oxide, electrolyte, can.)

Q:Explain Faraday's laws of electromagnetic induction

Answer: 

Michael Faraday discovered the principle of electromagnetic induction in 1831. It explains how an emf (electromotive force) is induced in a coil when magnetic flux linked with it changes.

Faraday’s First Law

• Whenever the magnetic flux ($\phi$) linking a closed circuit changes, an emf is induced in the circuit.

• The induced emf lasts only as long as the flux is changing.

• If the circuit is closed, this emf causes an induced current to flow

Faraday’s Second Law

• The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linkage.

Mathematically,$$e= -N \frac{dϕ}{dt}$$ where,  e = induced emf (volts)  N = number of turns in coil 𝜙  = magnetic flux (Wb) minus sign (–) shows Lenz’s Law (induced emf opposes the cause producing it).

Faraday’s laws form the basis of transformers, electric generators, and inductors, where emf is produced due to changing magnetic flux

Q:What is Lenz’s Law?

Answer

Statement
Lenz’s law states that the direction of the induced emf (and hence induced current) is always such that it opposes the change in magnetic flux that produced it.

Explanation:

When magnetic flux linked with a coil changes, an emf is induced (Faraday’s law). According to Lenz’s law, this induced emf produces a current whose own magnetic field opposes the original change in flux.

If flux increases → induced current produces flux in opposite direction.

If flux decreases → induced current produces flux in same direction to oppose reduction.

Mathematical form:

The negative sign in Faraday’s law shows Lenz’s law:$$e= -N \frac{dϕ}{dt}$$

Q:Deduce the relationship between line and phase voltage in a star connected system

Step 1 – Star connection basics

• In star connection, one end of each phase winding is joined to form the neutral (N) point.

• The other ends are connected to the line conductors (R, Y, B).

• Phase voltage ( Vph​ ) = Voltage between a line and neutral (e.g., VRN​).

• Line voltage ( VL​ ) = Voltage between any two lines (e.g., VRY​).

Express line voltage

              $$VR​=Vph​∠0∘$$ 

            $$VY​=Vph​∠−120∘$$

            $$VB​=Vph​∠−240∘$$

Now,

$${}_{}$$

$$VRY​=VR​−VY$$

Phasor subtraction 

$$V_R = V_{ph} \angle 0^\circ$$

$$V_Y​=V_{ph}\angle -120^\circ$$

$$VRY​=V_{ph} \angle 0^\circ−V_{ph}\angle -120^\circ$$ 

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Vph​(1+j0)−Vph(−21​−j23