23-07-2014, 07:34 PM
You said: Assume that the bulb is rated at 55 watts at a supply voltage of 12.6 volts.
From that, the resistance of the bulb at 12.6 volts can be calculated. What we now need to know is the relationship between the dissipated wattage of the bulb at different voltages - specifically, the new voltage of 14.4 volts. This will be produce a different value of resistance. The resistance of the connecting cables has been given. We are not told how the resistance of those cables varies with temperature - i.e. the heating effect of the current flowing through them - so we will have to assume that the resistance of them stays constant.
At that point, we know the resistance of the bulb for the two voltages; the resistance of the connecting cables (same for the two voltages) and the magnitude of those two voltages. Thus the two currents can be calculated; thus the voltage drop across the cables for the two voltages can be calculated.
The one critical piece of data that is missing in all of that is the relationship between the dissipated wattage of the bulb at different voltages. In practice, this could be easily derived by taking voltage and current measurements, but the Q. prohibits the use of meters.
Al.
From that, the resistance of the bulb at 12.6 volts can be calculated. What we now need to know is the relationship between the dissipated wattage of the bulb at different voltages - specifically, the new voltage of 14.4 volts. This will be produce a different value of resistance. The resistance of the connecting cables has been given. We are not told how the resistance of those cables varies with temperature - i.e. the heating effect of the current flowing through them - so we will have to assume that the resistance of them stays constant.
At that point, we know the resistance of the bulb for the two voltages; the resistance of the connecting cables (same for the two voltages) and the magnitude of those two voltages. Thus the two currents can be calculated; thus the voltage drop across the cables for the two voltages can be calculated.
The one critical piece of data that is missing in all of that is the relationship between the dissipated wattage of the bulb at different voltages. In practice, this could be easily derived by taking voltage and current measurements, but the Q. prohibits the use of meters.
Al.
