Fig. 6.2 shows the variation with time t of the current Ip in the primary coil. There is no current in the secondary coil.

Question 2

An ideal iron-cored transformer is illustrated in Fig. 6.1.

Fig. 6.1

(a) Explain why

(i) the supply to the primary coil must be alternating current, not direct current, [2]

(ii) for constant input power, the output current must decrease if the output voltage

increases. [2]

(b) Fig. 6.2 shows the variation with time t of the current Ip in the primary coil. There is no current in the secondary coil.

Fig. 6.2

Fig. 6.3

Fig. 6.4

(i) Complete Fig. 6.3 to show the variation with time t of the magnetic flux Φ in the

core. [1]

(ii) Complete Fig. 6.4 to show the variation with time t of the e.m.f. E induced in the

secondary coil. [2]

(iii) Hence state the phase difference between the current Ip in the primary coil and the

e.m.f. E induced in the secondary coil. [1]

Reference: Past Exam Paper – June 2005 Paper 4 Q6

Solution:

(a)

(i) The flux/field in the core must be changing so that an e.m.f./current is induced in the secondary.

(ii)

Power = VI

Since the output power is constant, if the (secondary) output voltage V_S increases, the (secondary) current I_S must decrease.

(b)

(i)

Graph has same shape and phase as I_P

(ii)

Graph:

same frequency, correct phase w.r.t. Fig. 6.3

{emf induced E = - dϕ / dt

The graph of ϕ is a sine curve. Differentiating sine gives cos. But since we have a negative sign, the cosine curve is inverted.}

(iii)

½π rad or 90°