= Solution
Use an <inverting operational amplifier>. Ground the non-inverting input, connect the source to the inverting input through $R_{\rm in}$, and connect $R_f$ from the output back to that same input.
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2017/paper-1-q4-inverting-amplifier.png]
{title=An ideal inverting amplifier with 10 kilohm input resistance and 100 kilohm feedback resistance}
In linear operation the ideal <operational amplifier> draws no input <electric current>, and feedback holds the inverting input at the same <electric potential> as the grounded non-inverting input. This node is a <virtual ground>. <Kirchhoff's current law> there gives
$$
\frac{V_i}{R_{\rm in}}+\frac{V_o}{R_f}=0,
\qquad
\frac{V_o}{V_i}=-\frac{R_f}{R_{\rm in}}.
$$
The source supplies current $I_i=V_i/R_{\rm in}$, so its <input impedance> is $R_{\rm in}$. The required design is therefore
$$
\boxed{R_{\rm in}=10\,\mathrm{k\Omega},\qquad R_f=100\,\mathrm{k\Omega},
\qquad V_o=-10V_i.}
$$
Only these two <resistors> and the single ideal <operational amplifier> are needed in the <signal> circuit; its power supplies are implicit. The result assumes an input small enough to keep the output within its linear operating range.
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