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GATE EE 2014 Official Paper: Shift 1

Option 3 : 2

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__ Concept__:

EMF equation of Transformer is given by \(E = \sqrt 2 \pi fϕ N\)

Where ϕ is the flux , given as \(ϕ = B \times A\)

__ Explanation__:

we know that,

An induced EMF in a transformer can be expressed as,

E = 4.44 fNϕ

\(∵ \frac{E}{f} = \rm constant\)

⇒ Nϕ = constant

⇒ ϕ ∝ \(\frac{1}{N}\) ....eq (1)

Now,

flux (ϕ) = \(\rm \frac{MMF}{Reluctance} = \frac{NI_m}{R} = \frac{NI_m}{l/\mu A}\)

⇒ \(\rm \phi = \frac{NI_m \mu A}{l}\)

From eq (1)

\(\rm ⇒ \frac{\mu I_m NA}{l} \propto \frac{1}{N}\)

⇒ \(\rm \frac{\mu N^2 AI_m}{l}\) = constant

⇒ N2ImA = constant

{∵ I0 (No-load current) = constant}

⇒ N2A = Constant

⇒ \(\rm N_1^2 A_1 = N_2^2 A_2\)

\(\Rightarrow \left( \frac{N_2}{N_1} \right)^2 = \left( \frac{r_1}{r_2} \right)^2 = \left( \frac{2r_2}{r_2} \right)^2\)

\(\left( \frac{N_2}{N_1} \right)^2 = 4\)

\(\frac{N_2}{N_1} = 2 \) i.e., Number of turns become double.