For an ideal op-amp shown, the value of R F to obtain a gain of 5

SOLUTION

Concept:

For non-inverting amplifier:

\({V_0} = \left( {1 + \frac{{{R_F}}}{{{R_1}}}} \right){V_i}\)

Calculation:

Using voltage division

\({V^ + } = {V_i}\left( {\frac{{2{\rm{k\Omega }}}}{{2{\rm{k\Omega }} + 1{\rm{k\Omega }}}}} \right) = \frac{2}{3}Vi\)

From virtual ground

V⁺ = V^- = 2/3 V_i

Apply nodal at V^-

\(\frac{{\frac{2}{3}{V_i} - 0}}{3} = \frac{{{V_0} - \frac{2}{3}{V_i}}}{{{R_1}}}\)  …1)

Given V₀ = 5V_i

\(\frac{{\frac{2}{3}{V_i}}}{3} = \frac{{5{V_i} - \frac{2}{3}{V_i}}}{{{R_F}}}\)

\(\frac{2}{9}{V_i} = \frac{{13{V_i}}}{{3{R_F}}}\)

\({R_F} = \frac{{13 \times 9}}{{3 \times 2}} = \frac{{39}}{2} = 19.5{\rm{\;k\Omega }}\)

R_F = 19.5 kΩ