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प्रश्न
Explain the working of the transformer.
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उत्तर
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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संबंधित प्रश्न
State the principle of the step-down transformer and its working.
Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer.
Explain the significance of Lenz’s law to show the conservation of energy in electromagnetic induction.
The following diagram in Fig.10.42 shows a coil of several turns of copper wire connected to a sensitive centre zero galvanometer G near a magnet NS. The coil is free to move in the direction shown in the diagram.
(i) Describe the observation if the coil is rapidly moved.
(ii) How would the observation be altered if (a) the coil has twice as many turns (b the coil was made to move three times as fast?
An ideal transformer has 100 turns in the primary and 250 turns in the secondary. The peak value of the AC is 28 V. The rms secondary voltage is nearest to ______
The primary of a transformer has 40 turns and works on 100 V and 100 W. Find a number of turns in the secondary to step up the voltage to 400 V. Also calculate the current in the secondary and primary.
Give the advantage of AC in long distance power transmission with an illustration.
A transformer having efficiency of 80% is working on 200 V and 6 kW power supply. If the current in the secondary coil is 6 A, the voltage across the secondary coil and the current in the primary coil respectively are ____________.
Magnetic flux passing through a coil is initially 4 × 10-4 Wb. It reduces to 10% of its original value in t second. If the emf induced is 0. 72 mV then t in second is ______.
