GATE EC 2015 Question Paper (31-Jan-2015) (Shift 2)

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a–b is ______________.

In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1V and 3V, respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached is ___________.

A dc voltage of $10\mathrm{V}$ is applied across an n – type silicon bar having a rectangular cross - section and a length of $1\mathrm{cm}$ as shown in figure. The donor doping concentration ${\mathrm{N}}_{\mathrm{D}}$ and the mobility of electrons ${\mu }_{\mathrm{n}}$ are $10^{-16}\mathrm{c}{\mathrm{m}}^{-3}$ and $1000\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1},$ respectively. The average time (in μsec) taken by the electrons to move from one end of the bar to other end is____________

In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100nm. The permittivities of the semiconductor and the oxide layer are ϵₛ and ϵₒₓ respectively. Assuming, $\frac{{\text{ϵ}}_{\mathrm{x}}}{{\text{ϵ}}_{\mathrm{ox}}}=3$, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is_____

The energy band diagram and the electron density profile n(x) in a semiconductor are shown in the figures. Assume that $\mathrm{n}\left(\mathrm{x}\right)=10_{\mathrm{e}}^{15}\left(\frac{\mathrm{qax}}{\mathrm{kT}}\right)\mathrm{c}{\mathrm{m}}^{-3}$, with $\alpha =0.1\mathrm{V}/\mathrm{cm}$ and x expressed in cm. Given $\frac{\mathrm{kT}}{\mathrm{q}}=0.026\mathrm{V},{\mathrm{D}}_{\mathrm{n}}=36\mathrm{c}{\mathrm{m}}^2{\mathrm{s}}^{-1},\mathrm{and}\frac{\mathrm{D}}{\mu }=\frac{\mathrm{kT}}{\mathrm{q}}$. The electron current density (in A/cm²) at x = 0 is