State Ohm’s law.

A lighting system is designed so that additional lamps can be added in parallel.

The diagram shows three 6V, 9W lamps connected in parallel to a supply of emf 6.0V and negligible internal resistance. A fuse in the circuit melts if the current in the circuit exceeds 13A.

(i) Determine the maximum number of lamps that can be connected in parallel in the circuit without melting the fuse.

(ii) Calculate the resistance of a lamp when operating at its normal brightness.

(iii) By mistake, a lamp rated at 12V, 9W is connected in parallel with three lamps rated at 6V, 9W. Estimate the resistance of the circuit stating any assumption that you make.

providing the temperature/physical conditions are constant and pd∝current;

or

providing the temperature/physical conditions are constant and the resistance is constant;

(i) current for one lamp =1.5 A;
\(\frac{{13}}{{1.5}} = 8.67\);
so 8;
Must show working for full credit. Allow any suitable method.

(ii) 4.0 Ω;

(iii) estimate:
resistance of incorrect lamp=16Ω;
total resistance of “correct” lamps in parallel =1.3Ω or \(\frac{1}{R} = \frac{1}{{16}} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}\);
total resistance=1.2Ω;

assumption:
“incorrect” lamp will be at correct resistance/working temperature/normal brightness;