The indicator (on the dashboard) has a resistance of 10.9 ω. the tank unit is a float connected to a variable resistor whose resistance varies linearly with the volume of gasoline. the resistance is 162 ω when the tank is empty and 24.4 ω when the tank is full. find the current in the circuit when the tank is (a) empty, (b) half-full, and (c) full. treat the battery as ideal.

I'm going to assume:

-- the indicator (on the dashboard) is in series with the tank unit;

-- the ideal battery is a lead-acid type, with terminal voltage of 13.6 VDC;

-- the car is wired with cryogenic superconducting wire, so there's no other resistance anywhere in the gas-gauge circuit.

Now I'll go ahead and solve the problem that I just invented.

a). when the tank is empty

-- indicator resistance = 10.9

-- tank unit resistance = 162

-- total circuit resistance = 172.9

Current in the circuit = V/R = (13.6 V) / (172.9 ) = 78.7 mA

b).  when the tank is half-full

-- indicator resistance = 10.9

-- tank unit resistance = (1/2) (162  +  24.4 )  =  93.2

-- total circuit resistance = 104.1

Current in the circuit = V/R = (13.6 V) / (104.1 ) =  130.6 mA

c).  when the tank is full

-- indicator resistance = 10.9

-- tank unit resistance = 24.4

-- total circuit resistance = 35.3

Current in the circuit = V/R = (13.6 V) / (35.3 ) = 385.3 mA

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