How Do You Calculate Current in a Half-Full Gasoline Gauge?

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To calculate the current in a half-full gasoline gauge, the resistance of the variable resistor must first be determined. The resistance when the tank is empty is 200 ohms, and when full, it is 30 ohms, indicating a linear relationship. For a half-full tank, the resistance is approximately 115 ohms, calculated as the average of 200 and 30 ohms. Using Ohm's Law (V=IR), where the voltage is 12V, the current can be calculated as I = V/R, resulting in a current of about 0.104 A. This approach clarifies how to find the current based on the varying resistance of the gauge.
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could anyone help me with this problem?

Homework Statement



An automobile gasoline gauge is shown schematically in Figure 27-61. The indicator (on the dashboard) has a resistance of 10 . The tank unit is a float connected to a variable resistor whose resistance varies linearly with the volume of gasoline. The resistance is 200 when the tank is empty and 30 when the tank is full.


*Find the current when the tank is half-full*

Homework Equations



V=IR

The Attempt at a Solution


the current when the tank is empty is 12=I*200. so i multiplied that by two to get the answer but it was incorrect. i also tried to plug 15 into the equation since it's half of thirty but that too was wrong
 

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First let's make a little chart to describe the variable resistor:

200 ohms ... tank empty
? ohms ... tank half-full
30 ohms ... tank full

What number should I replace those question marks with?
 
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