Why do some circuits have resistors connected directly to ground and how do I calculate its value

Why do some circuits have resistors connected directly to ground and how do I calculate its value

1.In digital/mixed-signal circuits you might find ~100kohm resistors connecting some nodes to GND (or VDD). These are pull-down (pull-up) resistors. Their purpose is to pull a node voltage down to GND (or up to VDD) if the node is not driven.

If the node is driven to a certain voltage then the driving voltage source should provide enough current to flow through the resistor. That is why the value of such resistors are chosen to be ~100kohm. Then a voltage source driving the node to say 1V only needs to provide 10uA for the resistor, which is a fairly small current.
2.The truth is that, to some extent, everything is connected to ground, it’s a circuit!, the name says it all. Except that is not shown at first sight.

You can calculate its value by its color code, measuring voltage at certain points, using Ohm’s Law, using Thevenin’s and Norton’s theorems, measuring current through certain paths.

You can approximate its value by knowing the type of circuit it is and finding on internet some application notes or other info about that circuit type.
3.No calculation required. In the circuit shown, the natural advantage of the high input impedance of the opamp is lost by a shunt 50 ohms and the input impedance of the overall circuit is just 50 ohm. And 50 ohm is the standard terminating impedance of the transmission line systems for maximum power transfer. Remember that the transmission lines operate at very high RF , in many GHz value and the connecting circuits should have this 50 ohm i/p and 50 ohm o/p impedances for correct line matching.
4.To calculate/know a resistors value you may:

Physically see the value marked on the resistor and assume that it is undamaged e.g. color codes or printed numbers or other codes.

Know the voltage across it and the current through it and using Ohm’s law as applicable to these values being AC or DC.

Remove all power and circuit connection(s) accomplish #2 using a digital multimeter which provides the voltage and measures the voltage across the test leads to “calculate” the resistance per #2. For AC a special meter may be required depending on the frequency and stray capacitance.

There are other specialized methods depending on the use of the resistor in the circuit and ascertaining its value indirectly.

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