GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

In the diagram shown, the frequency of the sinusoidal source voltage $V_s$ is 50 Hz. The load voltage is 230 V (RMS), and the load impedance is $\frac{230}{\sqrt{2}}+j\frac{230}{\sqrt{2}}\Omega$. The value of attenuator $A_1=\frac{1}{50\sqrt{2}}$. The multiplier output voltage $V_o=\frac{V_x{V}_y}{1V}$, where $V_x$ and $V_y$ are the inputs. The magnitude of the average value of the multiplier output $V_o$ is ________ V (rounded off to one decimal place).

In the circuit shown, assuming an ideal opamp, the value of the output voltage $V_o=$ ________ V (rounded off to one decimal place).

The rank of the matrix $A$ given below is one. The ratio $\frac{\alpha }{\beta }$ is ________ (rounded off to the nearest integer).

$A=\left[\begin{array}{cc}1& 4\\ -3& \alpha \\ \beta & 6\end{array}\right]$

A 1.999 V True RMS 3-1/2 digit multimeter has an accuracy of
$\pm 0.1$ % of reading $\pm 2$ digits.
It is used to measure 100 A (RMS) current flowing through a line using a 100:5 ratio, Class-1 current transformer with a burden of $0.1\Omega \pm 0.5$ %.,
The worst-case absolute error in the multimeter output is ________ V (rounded off to three decimal places).

The voltage source $V_s=10\sqrt{2}\sin (20000\pi t)$ V has an internal resistance of 50 $\Omega$. The RMS value of the current through R is ________ mA (rounded off to one decimal place).