For the operational amplifier circuit shown below, the output waveform \(V_{OUT}(t)\) is:
For a difference amplifier with input resistors \(R\) on each side, feedback resistor \(R_f\) on the inverting side and ground resistor \(R_g\) on the non-inverting side, the standard output is
\[V_{OUT} = \frac{R_f}{R}\left(\frac{1 + R/R_f}{1 + R_g/R}\right)V_2 - \frac{R_f}{R}V_1.\]With all four resistors equal (\(R_f = R_g = R\)) the expression collapses to the classical unity-gain subtractor:
\[V_{OUT}(t) = V_2 - V_1(t).\]Substituting \(V_2 = +2~\text{V}\) and \(V_1(t) = 2\sin(\omega t)~\text{V}\):
\[V_{OUT}(t) = 2 - 2\sin(\omega t)~\text{V}.\]Slot-by-slot evaluation over one period:
\[\begin{array}{|c|c|c|}\hline t & \sin(\omega t) & V_{OUT}(t)\\ \hline 0 & 0 & +2~\text{V}\\ T/4 & +1 & 0~\text{V}\\ T/2 & 0 & +2~\text{V}\\ 3T/4 & -1 & +4~\text{V}\\ T & 0 & +2~\text{V}\\ \hline\end{array}\]So \(V_{OUT}\) is a sine wave of peak-to-peak amplitude \(4~\text{V}\), riding on a \(+2~\text{V}\) DC offset, that starts at \(+2~\text{V}\) and moves downward first (because of the minus sign in front of \(\sin\omega t\)). It therefore swings between \(0~\text{V}\) and \(+4~\text{V}\), and this is the waveform in option (A), which matches the board key.
Similar Questions
For a given unijunction transistor (UJT) circuit peak voltage (\(V_p\)) is ...........
Symbols carry usual meaning.A rod \(AOB\) rotates in a vertical plane (the y-z plane) about a horizontal axis through \(O\) perpendicular to the plane (the x-axis) with constant angular velocity \(\omega\), as shown in the figure below. The equation of motion in \(r\) for a particle \(P\) of mass \(m\) constrained to move along the rod, assuming no frictional forces, is:
A particle \(P\) of mass \(m\) moves in the XY plane under the action of two forces, as shown in the figure below. \(\vec{F}_1\) is directed from \(P\) toward the fixed origin \(O\); \(\vec{F}_2\) is parallel to the positive x-axis. The angle between the position vector of \(P\) and the positive x-axis is \(\theta\). Using plane polar coordinates \((r,\theta)\) centred at \(O\), the equations of motion of the particle are:
In the logic-gate network shown below, the overall Boolean function realised at output \(Y\) is equivalent to which basic logic gate?
Consider a two-dimensional honeycomb lattice with nearest-neighbour (bond) distance \(a\), as shown in the figure below.
X-rays of wavelength \(\lambda\), when incident on the \((1\,0\,1)\) plane of a cubic lattice with lattice constant \(a\), produce a first-order Bragg reflection at \(\theta = 30^{\circ}\). The unit cell is then compressed along the z-axis so that its x and y edges keep length \(a\) while its z edge shortens to \(a/\sqrt{3}\), as depicted in the figure below.
The value of the line integral \(I = \int \vec{A}\cdot d\vec{r}\), where \(\vec{r} = x\hat{i} + y\hat{j}\) and \(\vec{A} = (x+y)\hat{i} + (y-x)\hat{j}\), along the path \(y^{2} = x\) from the point \((1, 1)\) to the point \((4, 2)\) is:
It is given that the residue of the complex function \(\dfrac{e^{1/z}}{z^{n}}\) at an isolated singular point \(z = 0\) is \(\dfrac{1}{9!}\). The value of \(n\) must be equal to:
A set \(V\) of complex numbers forms a two-dimensional real vector space under the usual addition of complex numbers and multiplication by real numbers. Let \(T : V \to V\) be a linear transformation defined as \(T(z) = \bar{z}\). Eigenvalues of \(T\) are:
The function \(f(x) = \exp(2x)\sin(2x)\) can be expanded as the Taylor series:
Important Questions from Mixed Topic (MH-SET)
Question: How did the Indian mythological film differ from the western biblical film in terms of presentation?
Question: What features distinguished the Indian mythological film from the western biblical film in terms of visual effects?
Question: What significant role does Georges Melies play in the Indian mythological film according to the paragraph?
For a given unijunction transistor (UJT) circuit peak voltage (\(V_p\)) is ...........
Symbols carry usual meaning.A rod \(AOB\) rotates in a vertical plane (the y-z plane) about a horizontal axis through \(O\) perpendicular to the plane (the x-axis) with constant angular velocity \(\omega\), as shown in the figure below. The equation of motion in \(r\) for a particle \(P\) of mass \(m\) constrained to move along the rod, assuming no frictional forces, is:
