One can measure the resistance of the front sensor, Bank 2 Sensor 1 without taking it out as it's right there in the front of the engine compartment. The back sensor, Bank 1 Sensor 1 is more difficult, but could also be measured without taking it out of car.
Do this when the engine is cold. Unplug the sensor from its socket. There's a small wire-tie you can undo to create more slack in the sensor wire to move it around.
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First is to simply use an ohmmeter and measure the resistance directly from the air/fuel sensor. The two leads to test are the two at the top. The top is indicated by the little nub that holds the sensor in place. Those two wires are black.
Although this method works ok to see if the sensor is bad, it doesn't take into the account the resistance of the wires you are testing with. And since the air/fuel sensor has such low readings, the small resistance the wires create can make a difference in an accurate reading or not.
Another method is called the Kelvin method. It cancels out the resistance of the test leads to get a more accurate reading.
Setup the wires as indicated in the diagram. For the extra wires (yellow/green), put each alligator clip the pins the black sensor wires.
Measure the amps and volts and write the numbers down. The numbers will fluctuate a little as the power is slowly drained from the battery. Do your best to get a simultaneous reading of both meters. Write the numbers down.
The photos below are from the house floor with the sensor out of the car. It's easier to trace the wires this way for illustration purposes.
Please note the meters in these photos are swapped; the ampmeter is on the right not on the left as in the wiring diagram.
Now that you have your data, you can perform the calculations:
----- = resistance (ohms)
Sample numbers from photos testing sensor in car:
1017 mV 1.017 V
--------- = --------- = 1.094 ohms
0.93 Amps 0.93 Amps
I don't have photos of testing the leads but here are the numbers used:
224.0 mV 0.224 V
--------- = --------- = 0.085 ohms
2.63 Amps 2.63 Amps
Finally, subtract the lead value from the sensor value to get the final measurement:
1.094 - 0.085 = 1.009 ohms which falls in range - good sensor!
There you have it. Salim and others will probably have something to add. This may be a red herring, as you can probably just get away with testing the sensor straight up and you'll know if it's bad or not. Anyway, I learned something.
I am bit lost reading the circuit [I under stand the purpose so read on ..]. My concern is short circuit current which can impact the voltage & current and the sensor is not protected against max current. As long as the voltage is low and the current capability is low things should be fine. Since 81corolla, has performed the tests, it seems the sensor is capable of taking that much current ... but use small size battery.
VOMs provide 'zeroing' capability but not all are equal. Get one which does a good job on low scale. They typically have a bridge circuit and protect the device under test.
Of course, you could touch the ohmeter leads together, record the reading (0.4 ohms for example), then do the real reading, move the test leads around for the best contact, record it and subtract the earlier reading from the test leads alone. that would get you pretty close to the real number.
BTW, in post #2, the picture showing the pins to connect to for ohmeter measurement were not correct for my sensor (bank 1 sensor 1, California emissions). (OBDII error codes 1133 and 1135). Maybe they are correct for other sensor locations. The diagram would be correct if the outside plastic spine facing downmost was a single, instead of a double, spine.
Also, when you go to the parts store, they will ask you "is your car California emissions?". You need to know, some are some aren't. Mine was (even though I live in MA). Look at the firewall, and see if you have a red placard saying something like "this car complies with California emissions".