Consider the vectors
$$ a=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], b=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] $$
For real-valued scalar variable $x$, the value of
$$ \min _x\|a x-b\|_2 $$
is___________(rounded off to two decimal places).
$\|\cdot\|_2$ denotes the Euclidean norm, i.e., for $y=\left[\begin{array}{l}y_1 \\ y_2\end{array}\right],\|y\|_2=\sqrt{y_1^2+y_2^2}$.
Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3 \Omega$ resistor are as indicated.
The voltage (in Volts) at node $X$ is __________ .
Let $i_C, i_L$, and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens(S). Which one of the following is true?
In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t)=100 \cos (200 t)$.
What should be the value of the variable capacitor $C$ such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A , respectively?
