In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{B}} \mathrm{L}^{\mathrm{O}} \mathrm{T}^{\mathrm{B}} \mathrm{A}^{\mathrm{S}}$, where value of 'Q' and 'R' are
An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is $100 \mu m \times 100 \mu m$. The distance between the plates $d_0 = 1 \mu m$ when both the capacitor charge and spring restoring force are zero as shown in Figure (a). A linear spring of constant $k = 0.01 N/m$ is connected to the movable plate. When charge is supplied to the capacitor using a current source, the top plate moves as shown in Figure (b). The magnitude of minimum charge (Q) required to momentarily close the gap between the plates is ________ $\times 10^{-14}$ C (rounded off to two decimal places).
Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is $\epsilon_0 = 8.85 \times 10^{-12}$ F/m and relative permittivity of air ($\epsilon_r$) is 1.
A 60 V DC source with an internal resistance \(R_{int} = 0.5 \, \Omega\) is connected through a switch to a pair of infinitely long rails separated by \(l = 1\) m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density \(B = 0.5\) T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is
For the circuit shown in the figure, the active power supplied by the source is ________ W (rounded off to one decimal place).
A signal $V_M = 5\sin(\pi t/3) V$ is applied to the circuit consisting of a switch S and capacitor $C = 0.1 \mu F$, as shown in the figure. The output $V_x$ of the circuit is fed to an ADC having an input impedance consisting of a $10 M\Omega$ resistance in parallel with a $0.1 \mu F$ capacitor. If S is opened at $t = 0.5 s$, the value of $V_x$ at $t = 1.5 s$ will be ________ V (rounded off to two decimal places).
Note: Assume all components are ideal.
In the circuit shown, the switch is opened at $t = 0$ s. The current $i(t)$ at $t = 2$ ms is ________ mA (rounded off to two decimal places).
In the circuit shown, the galvanometer (G) has an internal resistance of $100 \Omega$. The galvanometer current $I_G$ is ________ $\mu A$ (rounded off to the nearest integer).
The circuit given in the figure is driven by a voltage source $V_s = 25\sqrt{2}\angle 30^\circ V$. The system is operating at a frequency of 50 Hz. The transformers are assumed to be ideal. The average power dissipated, in W, in the $50 k\Omega$ resistance is ________ (rounded off to two decimal places).