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Can one do KCL at the ground node? Does any current go into the ground?

I think not, but I am not sure.

Bonus Question:

If yes, then how does grounding buildings drain the current into the Earth?

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You can use KCL at the ground node.

First, because in many circuits, the "ground" node is not actually connected to earth ground or to anything external circuit at all. It's just another circuit node that we use as reference for measuring potential at other nodes in the circuit.

Second, even when the circuit is externally grounded, there is the cut-set form of KCL. A cut set is any set of branches of a circuit that, if they were cut, would split the circuit into two disconnected circuits (but if any one of them were not cut while the others were, the circuit would remain connected). The cut-set form of KCL is:

KCL (cut-set law) For all lumped circuits, for all time t, the algebraic sum of the currents associated with any cut set is equal to zero.

(source)

What that means is, if you consider all the places where your circuit connects to earth ground, the net current through them is zero. So therefore KCL can be applied to all the places where other elements of your circuit connect to the local ground node.

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On most circuits, "ground" is just a lable we put on some point in the circuit to indcate that that point is considered as "zero volts", and is used as a reference when measuring voltages elsewhere in the circuit. I would prefer to call this point "common" or "reference" but the term "ground" is too well established to change.

This "ground" or "common" is just one node or connection point in a circuit and has no special magic properties, whether it is connected to earth or not.

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As we have total 4 nodes in the circuit...arrows are shown in the pic to show the direction of current ...the arrows coming towards a node is the entering current which we will add in the equation whereas the arrows going away from a node is the exiting current which we will subtract in the equation.The grounded node has no other path to enter or exit current...it is just to show the absorption of current.enter image description here

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