Advertisements
Advertisements
Question
Derive an expression for ratio of e.m.f.s and currents in terms of number of turns in primary and secondary coil.
Advertisements
Solution
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
RELATED QUESTIONS
State the principle on which transformer works.
Derive an expression for e.m.f. and current in terms of turns ratio
Express the turn ratio in terms of voltages.
Mention various energy losses in transformer device
On which type of current do transformers work?
State two factors on which the magnitude of induced e.m.f. depend.
In a transformer, the frequency of A.C. voltage ______.
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.
Mention the two characteristic properties of the material suitable for making core of a transformer.
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?
Draw a labeled diagram of a full wave rectifier circuit. State its working principle. Show the input-output waveforms ?
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.
What is the ideal transformer?
Can a transformer be used with direct current source? Give reason.
Name the principle on which functioning of a transformer depends.
What is the function of a step-up transformer?
Draw a labelled diagram to show the various parts of a step-up transformer and step down transformer.
(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 power supply to the primary coil of a transformer is 200 W. Find
(i) Current in primary coil if the e.m.f. supply to it is equal to 220V.
(ii) The number of turns in the primary coil is equal to 80 and that in secondary is 800. What is the transformation ratio?
(iii) Name the type of transformer.
(iv) What will be the output voltage?
(v) What is the current in the secondary coil for an ideal transformer?
(vi) What is the output power?
(vii) Is output and input power equal?
(viii) Compare the current flowing in a secondary coil and in a primary coil.
Applying e.m. f to primary coil is 210 V. If the number of turns in primary coil is 200 turns and that of in secondary coil is 20 turns, then find out the output voltage. Name the type of transformer.
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.
A circular coil of 100 turns with a cross-sectional area of 1 m2 is kept with its plane perpendicular to the magnetic field of 1 T. The magnetic flux linkage is ______.
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 ______
Transformer works on ______.
Explain the working of the transformer.
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 ____________.
A transformer works on the principle of ______.
For an ideal step-down transformer, the quantity which is constant for both the coils 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.
If the secondary coil has a greater number of turns than the primary, ______.
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.
A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The number of turns in the secondary in order to get output power at 230 V are ______.
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 voltage across the secondary coil is ______.
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 the bulb is ______.
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.
Power in primary coil is ______.
Define a Transformer.
The primary coil of a transformer has 800 turns and the secondary coil has 8 turns. It is connected to a 220 V ac supply. What will be the output voltage?
The primary winding of a transformer has 100 turns and its secondary winding has 200 turns. The primary is connected to an a.c supply of 120 V and the current flowing in its is 10 A. The voltage and the current in the secondary are ______.
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?
Electrical energy is transmitted over large distances at high alternating voltages. Which of the following statements is (are) correct?
- For a given power level, there is a lower current.
- Lower current implies less power loss.
- Transmission lines can be made thinner.
- It is easy to reduce the voltage at the receiving end using step-down transformers.
Draw the effective equivalent circuit of the circuit shown in figure, at very high frequencies and find the effective impedance.
1 MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if
- power is transmitted at 220 V. Comment on the feasibility of doing this.
- a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transfomer is used to bring voltage to 220 V. (ρCu = 1.7 × 10–8 SI unit)
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 ______.
An iron rod is placed parallel to magnetic field of intensity 2000 Am-1. The magnetic flux through the rod is 6 × 10−4 Wb and its cross-sectional area is 3 cm2. The magnetic permeability of the rod in Wb A-1m-1 is ______.
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 ______.
An iron rod of 0.2 cm2 cross-sectional area is subjected to a magnetising field of 1200 Am-1. If the susceptibility of iron is 599, then the magnetic flux produced is ______.
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 220 V ac voltage is applied to the primary coil, how much emf is induced in the secondary coil?
For what purpose are the transformers used?
