###### Advertisements

###### Advertisements

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 ‘N_{p}’ and ‘N_{s}’, respectively.

Therefore, the total magnetic flux linked with the primary coil at certain instant of time ‘t’ is N_{p}Φ. Similarly, the total magnetic flux linked with the secondary coil at certain instant of time ‘t’ is N_{s}Φ.

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.

Explain transformer working with construction.

Derive an expression for e.m.f. and current in terms of turns ratio

A transformer converts 240 V AC to 60 V AC. The secondary has 75 turns. The number of turns in primary are _______.

(A) 600

(B) 500

(C) 400

(D) 300

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.

Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer.

State the principle of transformer working with the help of a diagram

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 and two energy losses, giving the reasons for their occurrence in actual 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.

A transformer is used to step up an alternating emf of 200V to 440V. If the primary coil has 1000 turns, calculate the number of turns in the secondary coil.

An a.c generator generates an emf 'ε' where ε = 314 Sin (50πt) volt. Calculate the frequency of emf ε.

What is the turns ratio i.e., transformer ratio, n_{s}: n_{p}, in an ideal transformer which in-creases ac voltage from 220 V to 33000 V?

In an ideal transformer, an output of 66 kV is required when an input voltage of 220 V is available. If the primary has 300 turns, how many turns should the secondary have?

What is the ideal transformer?

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?

**Choose the correct option:**

A circular coil of 100 turns with a cross-sectional area of 1 m^{2} 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 ______

State the mathematical relation between a number of turns in the primary coil to a secondary coil in the step-up transformer.

Distinguish between Step up and Step Down Transformer.

What is Transformer?

Explain step up and step down transformer?

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.

Describe the construction and working of a transformer with a neat labelled diagram.

In a transformer, the number of turns in the primary and the secondary are 410 and 1230 respectively. If the current in primary is 6A, then that in the secondary coil is

A step-down transformer reduces the supply voltage from 220 V to 11 V and increase the current from 6 A to 100 A. Then its efficiency 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

What are step-up and step-down transformers?

Explain the working of the transformer.

Mention the various energy losses in a transformer.

Find out the phase relationship between voltage and current in a pure inductive circuit.

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 200V/120V step-down transformer of 90% efficiency is connected to an induction stove of resistance 40 Ω. Find the current drawn by the primary of the transformer.

The 300 turn primary of a transformer has resistance 0.82 Ω and the resistance of its secondary of 1200 turns is 6.2 Ω. Find the voltage across the primary if the power output from the secondary at 1600V is 32 kW. Calculate the power losses in both coils when the transformer efficiency is 80%

The output power in step-up transformer used in practice is ______.

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 ______.

**Assertion:** A transfonner cannot work on D.C. supply.

**Reason:** D.C. changes neither in magnitude nor in direction.

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 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 ______.

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 ______.

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 transformer is used ______

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 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 = (5t^{3} + 4t^{2} + 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 ______.

Magnetic flux Φ in weber in a closed circuit of resistance 10Ω varies with time Φ (sec) as Φ = 6t^{2} - 5t + 1. The magnitude of induced current at t = 0.25s is ______.

An ideal transformer converts 220 V a.c. to 3.3 kV a.c. to transmit a power of 4.4 kW. If primary coil has 600 turns, then alternating current in secondary coil is ______.

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 cm^{2}. The magnetic permeability of the rod in Wb A^{-1}m^{-1} is ______.

An iron rod of 0.2 cm^{2} 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 ______.

The primary coil having N_{P} turns of an ideal transformer is supplied with an alternating voltage V_{P}. Obtain an expression for the voltage V_{S} induced in its secondary coil having N_{S} turns.

The large scale transmission of electrical energy over long distances is done with the use of transformers. The voltage output of the generator is stepped-up because of ______.

Efficiency of transformer is the ratio of ______.

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 220 V ac voltage is applied to the primary coil, how much emf is induced in the secondary coil?

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.