Name: AC Voltage Applied to a Resistor
Uploaded: 2019-07-19
Duration: 7 min 45 s
Description: A purely resistive circuit has very little inductance at its typical frequency. This video explains various aspects of it and also shows the plotting of curr...

Question

Describe the principle, construction and working of a transformer.

Accepted Answer

Transformer is a device that is used in the power transmission of electric energy. Transformer works on the principle of mutual induction between two windings linked by common magnetic flux. When the source of alternating voltage is connected to the primary coil the magnetic flux produced in the primary coil induces flux in the secondary coil too. The frequency remains the same.

Construction: Transformer consists of two inducting winding and steel a core is laminated. The core is constructed by stacking sheets of steel with a minimum air gap between two. The steel is used because of its permeability and low hysteresis loss. The stacking must have alternating sides of the joint.

Working: Let the emf of the alternate current supplied by the $A C$ source be $E_{P} = E_{0} \sin (ω t)$

Let the primary windings be a pure inductance, so $I_{P}$ will lag behind the voltage $E_{P}$ by $90^{°}$ . Thus, the power factor for the primary coil becomes zero.

Let the number of turns in the primary coil be $N_{P}$ and secondary coil be $N_{s}$ .

According to Faraday law, the induced emf through one turn of both the coils will be the same.

Let the flux through one turn be $ϕ$ , the flux through the primary and secondary coil be $ϕ_{P}, ϕ_{s}$ respectively.

$ϕ_{P} = N_{p} ϕ$

$ϕ_{s} = N_{s} ϕ$

According to Faraday's law

$E = \frac{d ϕ}{d t}$

For primary coil $E_{P} = \frac{d ϕ_{P}}{d t} \dots (i)$

For secondary coil $E_{s} = \frac{d ϕ_{s}}{d t} \dots (ii)$

By dividing equation (i) by equation (ii)

$\frac{E_{P}}{E_{s}} = \frac{d ϕ_{P}}{d ϕ_{s}} = \frac{N_{P} ϕ}{N_{s} ϕ}$

$E_{P} = E_{s} \frac{N_{P}}{N_{s}}$

Power, $P = V I$

$P_{s} = E_{s} I_{s} \dots (iv)$

$P_{P} = E_{P} I_{P} \dots (v)$

For an ideal transfer no energy is lost, so

$P_{P} = P_{s}$

$E_{P} I_{P} = E_{s} I_{s}$

$I_{P} = \frac{E_{s}}{E_{P}} I_{s}$

$∵ \frac{E_{s}}{E_{P}} = \frac{N_{s}}{N_{P}}$

So, $I_{s} = \frac{N_{P}}{N_{s}} I_{P}$

Describe the principle, construction and working of a transformer.

Important Questions on Alternating Current

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