Essay S2 2019.docx

SECTION C [30 marks] Answer two questions only in this section 18. (a) State two functions of the dielectric in a capacitor. [2 marks] (b) Two pure capacitors with capacitance C1 = 5.0 F and C2 = 10.0 F are connected in series to a 10.0 V battery. (i) Derive an expression for the effective capacitance CT of the circuit and calculate the value of CT. [4 marks]

(ii) Calculate the total energy stored in the circuit. [2 marks] (c) The battery in (b) is replaced by an alternating current supply of maximum voltage 10 V and frequency 120 Hz. (i) Calculate the reactance of the combined capacitor. [2 marks] (ii) Calculate the maximum current in the circuit. Comment on the phase of the current with reference to the voltage supplied. [3 marks] (iii) Describe briefly the behaviour of the energy stored in the combined capacitor during a cycle of the alternating current supply. [2 marks] 19. (a) A magnetic field B passing through a horizontal wire loop PQRS of an area A and making an angle θ with the plane of the loop is shown in the diagram below.

(i) Express, in term of B, A and θ, the magnetic flux ϕ through the loop. [1 mark] (ii) State two alterations which can produce induced e.m.f n the loop. [2 marks] (iii) If the magnetic flux through the plane of the loop PQRS is reduced, what is the direction of the induced current in the loop? State the law used. [2 marks] (b) (i) Define self- inductance. [2 marks] (ii) An inductor in the form of solenoid has length 𝑙, cross-sectional area A and total turns N. Show that the self-inductance L is given by 𝜇0 𝑁 2 𝐴 𝑙 where 𝜇0 is the permeability of the free space. [2 marks] (c) A 50.0 Hz a.c generator consists of a coil of N turns and area 2.0 × 10−2 𝑚2 which rotates in a uniform magnetic field of 0.15 T. Calculate N so that the root mean square voltage produced is 240 V. [2 marks] (d) (i) At the moment an electric motor is switched on, a large amount of current flows in the armature and causes damage. Why does this happen? [1 mark] (ii) The electric motor is usually connected in series to an inductor to avoid the above situation from occurring. How can the inductor help avoid the damage? [2 marks] 𝐿=

20. (a) define the reactance of a pure inductor. [1 mark] (b) Derive an expression for the reactance XL, of a pure inductor in terms of it inductance L and the frequency f of a source of current supplied. [3 marks] [Assume that the expression of the source of current supplied is 𝐼 = 𝐼𝑜 𝑠𝑖𝑛2𝜋𝑓𝑡] (c) An a.c. circuit contains a pure inductor of inductance 0.470 mH. It is operated by a power supply with peak voltages of 120V and a frequency of 90.3 MHz. Determine the (i) the peak current of the inductor, [2 marks] (ii) the peak power in the inductor. [2 marks] (d) A capacitor has a Irms of 21 mA at a frequency of 60 Hz when the Vrms voltage across it is 14 V. (i) What is the capacitance of the capacitor? [3 marks] (ii) If the frequency is increased, will the current in the capacitor increase, decrease or stay the same? Explain. [2 marks] (iii) Calculate the Irms in the capacitor at a frequency of 410 Hz. [2 marks]

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…………………………… (PN WONG CHAI YEN)

…………………………………… (PN VONG SAY LEE) GPK Tingkatan 6