The "very close approximation" statement reflects the fact that for resistances in parallel, if one resistance is MUCH higher than the other, then their parallel combination as calculated with the formulas I described will be approximately the same number as the lower of the two resistances.
For the example you cited, using the reciprocal of the sum of the reciprocals formula (which applies to the parallel combination of any number of resistors):
1/(1/22 + 1/47000) = 21.9897 ohms.
Using the other formula I described, which applies to the specific case of exactly 2 resistors in parallel, gives the same result:
(22 x 47000)/(22 + 47000) = 21.9897 ohms.
21.9897 ohms is "to a very close approximation" equal to 22 ohms.
It's not that the 22 ohms "overrides" the 47K, it's that (based on the formulas) 47K becomes an insignificant contributor to the overall resistance when paralleled with a MUCH lower value.
Best regards,
-- Al
For the example you cited, using the reciprocal of the sum of the reciprocals formula (which applies to the parallel combination of any number of resistors):
1/(1/22 + 1/47000) = 21.9897 ohms.
Using the other formula I described, which applies to the specific case of exactly 2 resistors in parallel, gives the same result:
(22 x 47000)/(22 + 47000) = 21.9897 ohms.
21.9897 ohms is "to a very close approximation" equal to 22 ohms.
It's not that the 22 ohms "overrides" the 47K, it's that (based on the formulas) 47K becomes an insignificant contributor to the overall resistance when paralleled with a MUCH lower value.
Best regards,
-- Al