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ELEC102P PART I: PROBLEM SHEET 4

Question 1

(i) Derive an expression for the mutual inductance between two concentric circular loops

of radii  a  and  b   lying in the same plane if  b  >>  a. State any approximations you make.[The magnetic field at the centre of a circular loop of radius  r  carrying current   I  is  B  =

0 I /2r .]

(ii) If an ideal current source is connected to the  outer  loop and drives a current  I  =   I 0sint 

around it, derive an expression for the emf induced in the   inner   loop. How does this

depend on frequency?

(iii) If the wire used to form the loops has resistivity   and cross-sectional area   derive anexpression for the current that is circulating in the  inner  loop. Which way is this current

circulating with respect to the current in the outer loop?

(iv) What would happen to the induced emf and the circulating current in the inner loop if 

you increase the number of turns on the  outer  loop by a factor  N ?

(v) What would happen to the induced emf and the circulating current if instead you

increase the number of turns on the  inner  loop by a factor  N ?

(vi) The circuit above is essentially a simple transformer, but you probably found its

 behaviour differs from our analysis of transformers where the induced emf was the

same at all frequencies and depended on the turns ratio  N 2/ N 1. What is different about

the above circuit which is causing this difference?

Question 2

A transformer with 30 turns on the primary and 150 turns on the secondary is fed with a

sinusoidal signal of 15 V p-p. The secondary is open circuit. What is the rms value of the

voltage measured at the secondary?

Question 3

A transformer is used to match an antenna with a characteristic impedance of 12.5   to an

amplifier stage with an input impedance of 50  . What turns ratio should the transformer have?

Question 4

You want to use a transformer to efficiently couple an 8    speaker rated at 20 W to an audio

amplifier with an output impedance of 1 k 

(i) What turns ratio should you use?

(ii) What would be the current and potential difference in the secondary if the speaker is

run at full power?(iii) What would be the corresponding current and potential difference in the primary?

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Question 5

Why do we step up the voltage to transmit power from power stations? Isn’t the power 

dissipated in the lines going to go up as  V 2/ R  where  R  is their resistance? Hint: try sketching

the complete transmission circuit from power station to home.

Question 6

In the circuit below:

(a) find the magnitudes of  vs1 and  vs2;

(b) find the average power delivered to the primary;

(c) find the magnitude of   i p.

120V(peak)

75

turns

50

turns   v s1

1k   v s2

100

turns

500i p

120V(peak)

75

turns

50

turns   v s1

1k   v s2

100

turns

500i p