Question

Clark W. Griswold has been banned by his wife Ellen from any more home lighting projects during the holidays… but she never said anything about the car. Clark bought several boxes of 85W light bulbs and wires them into strands of five bulbs each in series.

He then connects the strands to his 12V car battery (in parallel) and tapes them to the body of his station wagon.  How many individual bulbs are used before Clark blows a 5A fuse connected to the battery?

Note: Use 110V for wall voltage.

Answer 1

as we know the wattage of any electrical component is described as,

here V is the wall voltage and R is the resistance of the component.

in this case since each strand is of resistance 5R and when two strands are connected parallely the resistance becomes 5R/2 and if three strands are connected in parallel the resistance becomes 5R/3. and so on

hence for x strands connected in parallel the total resistance becomes 5R/x.

so if no of strands is increased the total resistance will decrease accordingly, and according to ohms law the current flowing in the circuit will increase and once the current increases above 5A the fuse will blow.

in this case let the resistance of one light bulb be R

let us consider that x strands are used before the 5A fuse blows, from ohms law

Vb is the voltage of the car battery.

here the approximated value 297 is not taken because if x=297 then the current will exceed 5A

so the lower integer ie 296 is taken.

296 no of shards must be connected to parallel before the fuse blows or 296*5=1480 no of bulbs must be used