# How does current equal $i_o$ in this op amp problem?

I took a guess at this multiple choice question and got it right, however I'm not sure how current through the 1 kOhm resistor is equal to $$\i_o\$$?

I understand that for the ideal op amp, the voltages at both input nodes are equal to each other. However, because each of the voltages are divided across varying resistances, I do not understand how the 2 current values are equal. Can someone please help me understand this?

• Well, does current flow into ideal op-amp inputs or not? – Justme Mar 24 at 16:58
• Op amps are a new concept to me. So far, we have learned that 0 A flow into both inputs of an ideal op amp. So based on the wording of the question (current is flowing downwards through the 1 kOhm resistor) I imagined current flowing left to right through the 2 kOhm resistor and splitting at the node, with 0 A going into the op amp and the remaining current going into the 1 kOhm resistor. Since 0 A goes into the op amp, the 1 kOhm resistor takes all of the current coming from the 2 kOhm resistor. All of that being said, I still don't see how the 2 values are equal. – Vanidad Velour Mar 24 at 17:31
• Exactly, no current flows in to or out from the op-amp inputs. So there is only one path where the current flows. What does Kirchhoff's law of currents (KCL) state about currents in a circuit? – Justme Mar 24 at 17:36
• It is nicely illustrated in the answer below\ – Eugene Sh. Mar 24 at 17:38
• Ah ok...It clicked! I see it now. Thanks! – Vanidad Velour Mar 24 at 17:48

The trouble is that it looks like the set answer is wrong because the current into the 1 kΩ resistor is upwards and not downwards. So, the right answer should be $$\-i_0\$$ as I see it.
• $i_0$ exclusively feeds into the op-amp output. It is the value of $i_0$ that sets up the condition of the two op-amp inputs being ideally equal in voltage. $v_0$ dictates the current that flows in $R$. – Andy aka Mar 24 at 17:50