Advertisements
Advertisements
प्रश्न
Derive an expression for ratio of e.m.f.s and currents in terms of number of turns in primary and secondary coil.
Advertisements
उत्तर
Derivation:
Let ‘Φ’ be the magnetic flux linked per turn with both coils at a certain instant of time ‘t’.
Let the number of turns of the primary and secondary coils be ‘Np’ and ‘Ns’, respectively.
Therefore, the total magnetic flux linked with the primary coil at certain instant of time ‘t’ is NpΦ. Similarly, the total magnetic flux linked with the secondary coil at certain instant of time ‘t’ is NsΦ.
Now, the induced emf in a coil is
`e=(d phi)/dt`
Therefore, the induced emf in the primary coil is
`e_p=(d phi_p)/dt=(dN_p phi)/dt=-N_p(d phi)/dt` .......(1)
Similarly, the induced emf in the secondary coil is
`e_s=(d phi_s)/dt=(dN_s phi)/dt=-N(d phi)/dt` ........(2)
Dividing equations (1) and (2), we get
`e_s/e_p=(-N_s(d phi)/dt)/(-N_p(d phi)/dt)=N_s/N_p` ........(3)
The above equation is called the equation of the transformer and the ratio `N_s/N_p`is known as the turns ratio of the transformer.
Now, for an ideal transformer, we know that the input power is equal to the output
power.
∴`P_p=P_s`
∴`e_p i_p=e_s i_s`
∴`e_s/e_p=i_p/i_s`
From equation (3), we have
`e_s/e_p=N_s/N_P`
∴`e_s/e_p=N_s/N_p=i_p/i_s`
APPEARS IN
संबंधित प्रश्न
Derive an expression for e.m.f. and current in terms of turns ratio
Express the turn ratio in terms of voltages.
How much current is drawn by the primary of a transformer connected to 220 V supply when it delivers power to a 110 V − 550 W refrigerator?
Which coil of a step up transformer is made thicker and why?
Name two factors on which the magnitude of an induced e.m.f. in the secondary coil depends.
On which type of current do transformers work?
State two ways through which the strength of an electromagnet can be increased.
The secondary windings of a transformer in which the voltage is stepped down are usually made of thicker wire than the primary. Explain why.
A transformer is designed to work from a 240 V a.c. mains and to give a supply of 8 V to ring a house bell. The primary coil has 4800 turns. How many turns will be in the secondary coil?
The input and output voltage of a transformer are 220 V and 44 V respectively. Find: the turns ratio.
Describe, with the help of a suitable diagram, the working principle of a step-up transformer. Obtain the relation between input and output voltages in terms of the number of turns of primary and secondary windings and the currents in the input and output circuits.
State the underlying principle of a transformer. How is the large scale transmission of electric energy over long distances done with the use of transformers?
Describe briefly, with the help of labelled diagram, working of a step-up transformer.
A step-up transformer converts a low voltage into high voltage. Does it not violate the principle of conservation of energy? Explain.
The input and output voltages of a transformer are 220 V and 44V respectively. Find the current in input circuit if the output current is 2 A.
An a.c generator generates an emf 'ε' where ε = 314 Sin (50πt) volt. Calculate the frequency of emf ε.
Can a transformer be used with direct current source? Give reason.
(i) Draw a clear labelled diagram of an electric bell.
(ii) Explain in brief, its working.
(iii) What material is used for the core of an electric bell? State the reason.
The primary coil of a transformer has 200 turns while the secondary coil has 1000 turns. What type of transformer is this? if the input voltage is 10V, what will be the output voltage?
A transformer lowers e.m.f. 220 V to 12 volts. If the number of turns in primary are 8800, how many turns are in secondary coil?
A transformer lowers e.m.f. from 220 V to 15 V. If 400 W power is given in primary, calculate (i) the current in primary coil and (ii) the current in secondary coil.
The primary and secondary coils of a transformer each have an inductance of 200 x 10-6 H. The mutual inductance between the windings is 4 x 10-6 H. What percentage of the flux from one coil reaches the other?
Distinguish between Step up and Step Down Transformer.
Devices which is used to convert high alternating current to low alternating current is ______.
In a series resonant RLC circuit, the voltage across 100 Ω resistor is 40 V. The resonant frequency ω is 250 rad/s. If the value of C is 4 µF, then the voltage across L is
Explain the working of the transformer.
Mention the various energy losses in a transformer.
Give the advantage of AC in long distance power transmission with an illustration.
Find out the phase relationship between voltage and current in a pure inductive circuit.
The output power in step-up transformer used in practice is ______.
Which among the following, is not a cause for power loss in a transformer?
Read the following paragraph and answer the question:
Long distance power transmissions
The large-scale transmission and distribution of electrical energy over long distances is done with the use of transformers. The voltage output of the generator is stepped up. It is then transmitted over long distances to an area sub-station near the consumers. There the voltage is stepped down. It is further stepped down at distributing sub-stations and utility poles before a power supply of 240 V reaches our homes.
We need to step-up the voltage for power transmission, so that ______.
A transformer is essentially an a.c. device. It cannot work on d.c. It changes alternating voltages or currents. It does not affect the frequency of a.c. It is based on the phenomenon of mutual induction. A transformer essentially consists of two coils of insulated copper wire having different numbers of turns and wound on the same soft iron core.
The number of turns in the primary and secondary coils of an ideal transformer is 2000 and 50 respectively. The primary coil is connected to a main supply of 120 V and secondary coil is connected to a bulb of resistance 0.6 Ω.
The value of current in primary coil is ______.
A step-down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
Draw the effective equivalent circuit of the circuit shown in figure, at very high frequencies and find the effective impedance.
A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be:
The magnetic flux through a coil perpendicular to its plane is varying according to the relation Φ = (5t3 + 4t2 + 2t - 5) Weber. If the resistant of the coil is 5 ohm, then the induced current through the coil at t = 2 sec will be ______.
Efficiency of transformer is the ratio of ______.
The primary coil of a transformer has 60 turns whereas its secondary coil has 3000 turns.
If a current of 5A flows in the primary coil, how much current will flow in a load in the secondary coil? State the assumption you have made regarding the transformer, in this calculation.
What is a transformer?
Derive the equation for a transformer.
Explain why core of a transformer is always laminated.
A step down transformer connected to an AC mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
A 12 V, 60 W lamp is connected to 220 V AC via an ideal transformer. Find the primary current.
In an ideal transformer, the turns ratio is `N_p/N_s = 1/2`. The ratio Vs : Vp is equal to (the symbols carry their usual meaning):
On which principle is a transformer based?
How is the laminated soft iron core made?
Which description of the primary coil is correct?
What does the primary coil draw from the source?
Which winding is the output coil connected to the load?
What does the secondary coil deliver to the circuit?
What do \[V_s\] and \[V_p\] represent?
