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Question
Explain the working of the transformer.
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Solution
Principle:
The principle of a transformer is the mutual induction between two coils. That is, when an electric current passing through a coil changes with time, an emf is induced in the neighbouring coil.
Working:
- If the primary coil is connected to a source of alternating voltage, an alternating magnetic flux is set up in the laminated core.
- If there is no magnetic flux leakage, then the whole magnetic flux linked with primary coil is also linked with the secondary coif This means that rate at which magnetic flux changes through each turn is same for both primary and secondary coils.
- As a result of flux change, emf is induced in both primary and secondary coils. The emf induced in the primary coil εp is almost equal and opposite to the applied voltage υp and is given by
υp = εp = -Np `("d" Φ_"B")/"dt"` .....(1) - The frequency of alternating magnetic flux in the core is the same as the frequency of the applied voltage. Therefore, induced emf in secondary will also have the same frequency as that of applied voltage.
- The emf induced in the secondary coil eg is given by
εs = -Ns `("d" Φ_"B")/"dt"`
where Np and Ns are the number of turns in the primary and secondary coil, respectively. If the secondary circuit is open, then εs = υs where υs is the voltage across secondary coil.
υs εs = -Ns `("d" Φ_"B")/"dt"` .....(2)
From equation (1) and (2),
`"v"_"s"/epsilon_"s" = "N"_"s"/"N"_"p"` = K ....(3)
This constant K is known as voltage transformation ratio. For an ideal transformer,
Input power υp ip = Output power υsis
where iυp and is are the currents in the primary and secondary coil respectively. Therefore,
`"v"_"s"/"v"_"p" = "N"_"s"/"N"_"p" = "i"_"p"/"i"_"s"`
Equation (4) is written in terms of amplitude of corresponding quantities,
`"V"_"s"/"V"_"p" = "N"_"s"/"N"_"p" = "I"_"p"/"I"_"s"` = K ....(4)
(i) If Ns > Np ( or K > 1)
∴ Vs > Vp and Is < Ip.
This is the case of a step-up transformer in which voltage is decreased and the corresponding current is decreased.(ii) If Ns < Np (or K < 1)
∴ Vs < Vp and Is > Ip
This is a step-down transformer where voltage is decreased and the current is increased.
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