GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

One coulomb of point charge moving with a uniform velocity 10 $\hat{x}$ m/s enters the region x ≥ 0 having a magnetic flux density$\overrightarrow{B}=\left(10y\hat{x}+10x\hat{y}+10\hat{z}\right)T$. The magnitude of force on the charge at x = 0⁺ is ______ N.

($\hat{x}$, $\hat{y}$ and $\hat{z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively.)

In the given circuit, for maximum power to be delivered to R${}_L$, its value should be ______ Ω. (Round off to 2 decimal places.)

Inductance is measured by

The bode magnitude plot for the transfer function $\frac{V_0(s)}{V_i(s)}$ of the circuit is as shown. The value of R is ______ Ω. (Round off to 2 decimal places.)

In the given, figure, plant $G_p(s)=\frac{2.2}{(1+0.1s)(1+0.4s)(1+1.2s)}$ and compensator $G_c(s)=K\left(\frac{1+T_{1}s}{1+T_{2}s}\right)$. The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is ______. (Round off to 2 decimal places.)