= Solution
The ideal voltage-feedback <Operational amplifier> has \b[zero input currents] and, while stable <negative feedback> holds it in its linear operating range, \b[equal input voltages]: $i_+=i_-=0$ and $v_+=v_-$. The first rule follows from infinite <input impedance>; the second is the large-open-loop-gain limit of $v_o=A(v_+-v_-)$. Equal input <electric potential> is a <virtual short>, not an electrically conducting connection.
For an <inverting amplifier> with the noninverting input grounded, $v_-=0$ and node-current balance gives $v_i/R_i=-v_o/R_f$, hence \b[$v_o=-R_fv_i/R_i$]. For a <noninverting amplifier>, the feedback divider gives $v_-=v_oR_g/(R_f+R_g)=v_i$, hence \b[$v_o=(1+R_f/R_g)v_i$].
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2016/paper-1-op-amp-feedback.png]
{title=Ideal inverting and noninverting negative-feedback configurations}
{source=paper-1-op-amp-feedback.py}
One should check output swing, input common-mode range, <slew rate>, <Gain-bandwidth product> and stability before using these limits in a real circuit. Saturation, positive feedback or operation beyond <bandwidth> invalidates the equal-voltage rule; finite input bias currents and offset voltage can also matter.<Operational-amplifier negative feedback by Analog Devices>[University electronics course, Chapter 3: high-gain feedback assumptions and practical limits]{ref}
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