A simple ac generator has a rectangular coil of 150 turns, each of area 4.0 × 10$^{-3}$ m$^2$. The coil rotates at 50 revolutions per second in a uniform magnetic field of flux density 0.080 T.
(a) Calculate the peak emf induced in the coil. [2]
(b) The rotation frequency is doubled. State and explain the effect on the peak emf. [2]
(c) A step-down transformer has 1150 turns on its primary coil. The primary coil is connected to a 230 V supply and the output pd of the secondary coil is 12 V. Assume the transformer is ideal for part (i).
(i) Calculate the number of turns on the secondary coil. [1]
(ii) Explain why the core of the transformer is laminated. [2]
- (a) $\varepsilon_0 = BAN\omega$ with $\omega = 2\pi \times 50$(1)
- (a) $\varepsilon_0 = 0.080\times4.0\times10^{-3}\times150\times314$ = 15 V (15.1)(1)
- (b) peak emf doubles (to 30 V)(1)
- (b) because the rate of change of flux linkage doubles (Faraday's law) (accept $\varepsilon_0 \propto \omega$)(1)
- (c)(i) $N_s = N_p\frac{V_s}{V_p} = 1150\times\frac{12}{230}$ = 60(1)
- (c)(ii) laminations (thin layers insulated from each other) reduce eddy currents in the core (accept 'increase resistance to eddy currents')(1)
- (c)(ii) so less energy is wasted heating the core / transformer is more efficient(1)
- Answer: (a) 15 V (b) doubles to 30 V (c)(i) 60 turns
- Examiner tip: In (b), name the cause: rate of change of flux linkage — 'it spins faster' alone doesn't score.