For the non-inverting amplifiers as shown, find the closed-loop voltage gain.

Concept of Virtual Ground:

• The differential input voltage Vid between the noninverting and inverting input terminals is essentially zero.
• This is because even if the output voltage is few volts, due to a large open-loop gain of the op-amp, the difference voltage Vid at the input terminals is almost zero.

Where Vid is differential voltage, Vin1 is noninverting voltage, Vin2 is inverting voltage.

If the output voltage is 10 V and A i.e., the open-loop gain is 104 then, 

V out = A Vid

Vid = V out / A

= 10 / 104

= 1 mV.

Hence Vid is very small, for analyzing the circuit assumed to be zero.

Vid = Vin1 - Vin2

(Vin1 - Vin2) = V out / A

= V out / ∞ = 0

Calculation:

Circuit diagram:

Two terminals of Op-Amp i.e.; Inverting Terminal and Non-Inverting Terminal are at equipotential.

Apply KCL at node 1V_pp,

\(\frac{{1{V_{pp}} - 0}}{{10\;k}} + \frac{{1{V_{pp}} - {V_0}}}{{100k}} = 0\)

\(\frac{{10{V_{pp}} + 1{V_{pp}} - {V_0}}}{{100K}} = 0\)

\(11{V_{pp}} - {V_0} = 0\)

Closed-loop gain is given by the ratio of output to the input.

so the Closed-loop voltage gain is given by,

\(\frac{{{V_0}}}{{{V_{pp}}}} = 11\)