Problem #0131 Electricity & Magnetism Sub-menu Problem #0133 Chapters Chapters

402.

Problem 33.6 (RHK)

A gasoline gauge for an automobile is shown schematically in the figure. The indicator (on the dashboard) has a resistance of . The tank is simply a float connected to a resistor that has a resistance of when the tank is empty, when it is full, and varies linearly with the volume of gasoline. We have to find the current in the circuit when the tank is (a) empty, (b) half full, and (c) full.

Solution:             Click For PDF Version

We note the data of the problem:

We will apply Ohm’s law in finding the current in the circuit with different total resistances.

(a)

Resistance in the circuit when the tank is empty will be Current in the circuit when the tank is empty will be

(b)

Resistance in the circuit varies linearly with the volume of gas in the tank. Let the volume of the full tank be V. From the values of and , we note that the linear equation giving the resistance as a function of volume of gas in the tank will be

When the tank is half full, the volume of the gas will be , and the resistance of the fuel tank will be The total resistance in the circuit in this situation will be

(c)

When the tank is full the total resistance in the circuit will be

And