Kirchoff's current law question

[bitrex]

I'm looking at the derivation of a band pass filter circuit, and part of the circuit is a capacitor and resistor in parallel from the non-inverting input to the output. My thinking is that the current through the capacitor is going to be the current coming in (since the inverting input draws no current) minus the current going through the resistor, or Ic = I - Ir. Nope, the derivation has it the other way, Ic = Ir - I. I can't figure out why this is.

 

[tenacity2986]

depends on the standardization of current. If current is defined as direction holes travel in, than it follows passive sign convention whereas, current is usually defined as direction opposite of electron flow. I see your point. Ic + Ir = I so
Ic = I - Ir...

 

[oswaler]

I can explain the reasoning behind the derivation of Kirchoff's current law in this situation. Kirchoff's current law states that the sum of currents entering and exiting a node in a circuit must be equal. In this band pass filter circuit, the non-inverting input is considered a node.

When looking at the current through the capacitor, it is important to consider the direction of the current. Since the non-inverting input draws no current, the current entering the node is equal to the current exiting the node. This means that the current through the capacitor, Ic, must be equal to the current going through the resistor, Ir, minus the current coming in, I. This can also be written as Ic = Ir - I.

The reason for this is that the current through a capacitor is in the opposite direction of the voltage change across it. In this circuit, the voltage change across the capacitor is the same as the voltage change across the resistor, but in the opposite direction. Therefore, the current through the capacitor must also be in the opposite direction of the current through the resistor.

I hope this explanation helps clarify the derivation of Kirchoff's current law in this particular circuit.