Questions & Answers (Hints) - 1

Question   (14 marks)

Following figure shows how the potential difference across the terminals of two different lamps, A and B, varies as the current through them is varied. 

The lamps are both designed to operate normally when the potential difference across them is 12.0 V.

(a)  Following figure shows a potentiometer. Complete the circuit to show how you would connect a 12 V supply, one of the lamps, an ammeter, and a voltmeter to enable observations to be made over the full range of voltages between 0 and 12 V.   (2 marks)

(b)  Explain briefly why the lamps have a non-linear variation of potential difference with current.   (4 marks)

(c)  Determine the resistance of lamp A when operating normally.   (3 marks)

(d)  Lamps A and B are connected in series to a 24 V supply. The current is measured and found to be 1.5 A.

Determine, showing your reasoning clearly:

      (i)  the terminal potential difference of the supply;   (3 marks)

      (ii)  the internal resistance of the supply.   (2 marks)

Answer

(a)  Correct arrangement for battery and lamp using potential divider, ammeter in circuit and voltmeter across;

(b)  Heating effect of current, as current increases the temperature of filament rises; as temperature rises so does resistance; because lattice vibrations increase so more electron collisions; V/I increases so graph is non-linear.

(c)  3.0 A; R(= V/I) = 12/3 = 4 Ω;

(d)(i)  p.d. across lamp A when current is 1.5 A = 4.4 V or R = 2.9 Ω;
           p.d. across lamp B when current is 1.5 A = 5.8 V or R = 3.8 Ω; addition = 10.2 V;

(d)(ii)  E = V - Ir; = (24 - 10.2)/1.5 = 9.3 Ω;