Q24 of 26 Page 1

(i) Draw a labelled diagram of a step-down transformer. State the principle of its working. (ii) Express the turn ratio in terms of voltages. (iii) Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer.

(iv) 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?


OR


(a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.


(b) A rectangular coil of area A, having number of turns N is rotated at ' f ' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 rf NBA.

(i) Principle:


A transformer works on the principle of mutual induction. If the amount of flux inside the primary coil changes , a corresponding emf is induced in the secondary coil.


Working:


In a step down transformer, A primary coil with high number of turns and thus high voltage and low current is connected to an alternating current source , the current changes continuously in this coil, which in turn changes the magnetic flux through the secondary coil continuously. An alternating of low emf , though of same frequency is developed across the secondary terminals.


The faraday’s law of e.m.f induced in the primary coil can be written as:


…..(a)


Where,


E is the emf induced in the primary coil,


N is the number of turns of coil


ϕ is the flux through the coil


And the e.m.f induced in the secondary coil is given as:


…….(b)


Where,


E’ is the emf induced in the secondary coil,


N’ is the number of turns of secondary coil,


ϕ is the flux through the coil.


On dividing (a) and (b) we get,



For step down transformer we have, C<1


Therefore, E’ < E



(ii) The emf induced in the primary coil can be given as:


…..(a)


Where,


E is the emf induced in the primary coil,


N is the number of turns of coil


ϕ is the flux through the coil


And the e.m.f induced in the secondary coil is given as:


…….(b)


Where,


E’ is the emf induced in the secondary coil,


N’ is the number of turns of secondary coil,


ϕ is the flux through the coil.


On dividing (a) and (b) we get,



Where,


C is called the turn ratio or the transformation ratio.


(iii) If the transformer is ideal , then


The input electrical power is equal to the output electrical power.


EI = E’I’


Where,


E, E’ is the emf induced in primary and secondary coil respectively,


I and I’ is the current in the primary and secondary coil respectively.


Therefore, we get



Where,


C is called the turn ratio or the transformation ratio.


(iv) The power can be defined as:


Power = Vp× Ip


Where,


Vp is the emf od primary coil,


Ip is the current in the primary coil.


Given,


Power = 550 W


The voltage supplied , V = 220 V


⇒ Ip = 550 W / 220 V = 2.5 A


OR


(a) If two inductors are placed in proximity, and when the time varying current in one inductor changes, the flux changes with it and thus cuts the inductor nearby , which in response produces a onduced voltage in both the inductors.


We consider coils P and Q . We take a time varying current I flowing through one of the coils, let it be P, then we get,


ϕ α I


ϕ = MI


where,


ϕ is the magnetic flux through the coil


M is the coefficient of mutual inductance,


The induce emf can be written as:



We take mutual inductance of the coils of radius r1 and r2 such that, r1 < r2, and place the two coils coaxially, we have,


Φ21 α I ,


⇒ ϕ21 = M2 I1


Where ,


M2 is the coefficient of mutual inductance of two coils.


The magnetic field of the first coil can be given as:


B1 = μn1I1


Where,


Magnetic flux linked with the second coils B1 times the cross section of the first coil.


Thus, ϕ21 = B1A × n2I


⇒ ϕ21 = μn1I1× A× n2I


⇒ ϕ21 = μn1n2 AI I1


⇒ M21 = μn1n2 AI


Thus similarly we can have:


M12 = μn1n2AI


And then


We have, M12 = M21 = M


M = μn1n2AI


(a) The number of turns on the rectangular coil is supposed to be N . Let A be the cross sectional area which is placed under the magnetic field of magnitude B, The magnetic flux linked with coil can be given as:


ϕ = NBA cosθ


Thus, the emf induced in the coil can be given as:


E = -dϕ /dt


⇒


⇒ E = NBA.sin θ (2πf)


Where,



We can see, For maximum emf induced we must have ,


Sinθ = 1,


Therefore,


E = NBA (2πf)


Which is the maximum emf induced in the coil.


More from this chapter

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22

Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.

Draw the magnetic field lines due to a circular wire carrying current I.

 23

Ram is a student of class X in a village school. His uncle gifted him a bicycle with a dynamo fitted in it. He was very excited to get it. While cycling during night, he could light the bulb and see the objects on the road. He, however, did not know how this device works. He asked this question to his teacher. The teacher considered it an opportunity to explain the working to the whole class. Answer the following questions:

(a) State the principle and working of a dynamo.


(b) Write two values each displayed by Ram and his school teacher.

 25

(i) Derive the mathematical relation between refractive indices n1 and n2 of two radii and radius of curvature R for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index n1 and a real image formed in the denser medium of refractive index n2. Hence, derive lens maker's formula.

(ii) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?


OR


(a) Draw a labeled ray diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.


(b) You are given three lenses of power 0.5 D, 4 D and 10 D to design a telescope.


(i) Which lenses should he used as objective and eyepiece? Justify your answer.


(ii) Why is the aperture of the objective preferred to be large?

 26

(i) Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?

(ii) Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C1 and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.


OR


(i) If two similar large plates, each of area A having surface charge densities + and —are separated by a distance d in air, find the expressions for


(a) field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.


(b) the potential difference between the plates.


(c) the capacitance of the capacitor so formed.


(ii) Two metallic spheres of radii R and 2R are charged so that both of these have same surface charge density. If they are connected to each other with a conducting wire, in which direction will the charge flow and why?