The circuit you have, as drawn, is sending a low current, low power, voltage signal. That bit is important- a SIGNAL which means to transmit information (like data, commands) but not power or current. As a signal it implies low power since your goal is to transmit information rather than power and to conserve power you make it as low power as possible.
And it's a voltage signal, so it's not even a current signal that uses small varying levels of current to send information, but a voltage signal which means as close to zero current as possible (to conserve power). In that case you use much larger resistors (kohms) and much smaller transistors since your goal is to transmit a signal, not power so you want to save power.
So the circuit as you have drawn is only correct if you are trying to send a voltage signal to your fuel injector, possibly to command it turn on or off, but not to power it or connect and disconnect it from the power source.But like I said earlier, in that case you use large resistors and small low current MOSFETs and your MOSFET is enormous which leads me to think you are just trying to shut power on or off to the fuel injector.
To actually pass current and power through the injector, there actually is no resistor, but the circuit is wrong. Removing the resistor in your circuit just makes a short-circuit whenever the transistor turns on which bypasses the injector, providing it no power or current, and blows up your battery and MOSFET at the same time.
The proper circuit is this:
+12V----->Fuel Injector----->(Drain)NMOS(Source)------>GND
I replaced your MOSFET with an NMOS, which is the most common type of MOSFET and the easiest to work with in the position shown. The alternative is:
+12V----->(Source)PMOS(Drain)---->Fuel Injector----->GND
Technically you can use either a PMOS or NMOS in any of those two positions (ie. an NMOS closest to +12V or a PMOS closest to GND), but it is not as natural to generate the required gate signal for the MOSFET (the third pin which controls whether the transistor is on or off). For your reference, here are those two circuits:
+12V----->Fuel Injector----->(Source)PMOS(Drain)------>GND
+12V----->(Drain)NMOS(Source)---->Fuel Injector----->GND