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.
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.
Write the function of a transformer.
A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 300 turns. Find the number of turns in the secondary to get the power output at 220 V.
Which coil of a step up transformer is made thicker and why?
Name the transformer used in the power transmitting station of a power plant.
What type of current is transmitted from the power station?
Name two factors on which the magnitude of an induced e.m.f. in the secondary coil depends.
The teachers of Geeta’s school took the students on a study trip to a power generating station, located nearly 200 km away from the city. The teacher explained that electrical energy is transmitted over such a long distance to their city, in the form of alternating current (ac) raised to a high voltage. At the receiving end in the city, the voltage is reduced to operate the devices. As a result, the power loss is reduced. Geeta listened to the teacher and asked questions about how the ac is converted to a higher or lower voltage.
1) Name the device used to change the alternating voltage to a higher or lower value. State one cause for power dissipation in this device.
2) Explain with an example, how power loss is reduced if the energy is transmitted over long distances as an alternating current rather than a direct current.
3) Write two values each shown by the teachers and Geeta.
You are required to make an electromagnet from a soft iron bar by using a cell, an insulated coil of copper wire and a switch. (a) Draw a circuit diagram to represent the process. (b) label the poles of the electromagnet.
Complete the following sentence :
……… energy is converted into …………energy by an electric motor.
Explain why an induced current must flow in such a direction so as to oppose the change producing it.
For what purpose are the transformers used? Can they be used with a direct current source?
Why is the iron core of a transformer made laminated (thin sheets) instead of being in one solid piece?
The transformer is used in ______ current circuits.
In a transformer, the frequency of A.C. voltage ______.
Name two kind of energy loss in a transformer. How is it minimized?
The primary coil of a transformed has 800 urns and the secondary coil has 8 turns. It is connected to a 220 V a.c. supply. What will be the output voltage?
Given the input current 15 A and the input voltage of 100 V for a step-up transformer having 90% efficiency, find the output power and the voltage in the secondary if the output current is 3 A.
Mention the two characteristic properties of the material suitable for making core of a transformer.
State the principle of working of a transformer. Can a transformer be used to step up or step down a d.c. voltage? Justify your answer.
Draw a labeled diagram of a full wave rectifier circuit. State its working principle. Show the input-output waveforms ?
What is the turns ratio i.e., transformer ratio, ns: np, in an ideal transformer which in-creases ac voltage from 220 V to 33000 V?
What is the function of a step-up transformer?
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.
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 ______
State the mathematical relation between a number of turns in the primary coil to a secondary coil in the step-up transformer.
Explain step up and step down transformer?
Describe the construction and working of a transformer with a neat labelled diagram.
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 construction of transformer.
A step-down transformer connected to the main supply of 220 V is used to operate 11V,88W lamp. Calculate
- Voltage transformation ratio and
- Current in the primary
A 220 V input is supplied to a transformer. The output circuit draws a current of 2.0 A at 440 V. If the ratio of output to input power is 0.8, then the current drawn by primary winding is ______.
A 100% efficient transformer has 100 turns in the primary and 50 turns in its secondary coil. If the current in the secondary coil is 6 A, then the current in the primary coil 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.
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.
Power in primary coil is ______.
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?
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:
A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10 A, then the input voltage and current in the primary coil are ______.
In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current in primary coil is 4 A, then that in the secondary coil is ______.
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 ______.
Mention two main sources of power loss in real transformers.
The self-inductance of a closely wound coil of 200 turns is 10 mH. Determine the value of magnetic flux through the cross-section of the coil when the current passing through the coil is 4 mA.
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.
Derive the equation for a transformer.
