Two batteries of emf's \(3V \& 6V\) and internal resistances 0.2 Ω \(\&\) 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find:
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination
In the given circuit, the potential difference across the plates of the capacitor \( C \) in steady state is
A feedback control system is shown in the figure.
The maximum allowable value of \( n \) such that the output \( y(t) \), due to any step disturbance signal \( d(t) \), becomes zero at steady-state, is ________ (in integer).
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 schematic of a Michelson interferometer, used for the measurement of refractive index of gas, is shown in the figure. The transparent chamber is filled with a gas of refractive index $n_g$, where $n_g \neq 1$, at atmospheric pressure. If a 532 nm laser beam produces 30 interference fringes on the screen, then the number of fringes produced by a 632.8 nm laser beam will be ________ (rounded off to one decimal place). Note: Assume that the effect of beamsplitter width is negligible. The setup is placed in air medium with refractive index equal to 1.