GATE EC 2015 Question Paper (31-Jan-2015) (Shift 1)

In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of ${\mathrm{V}}_{\mathrm{c}}\left(\mathrm{t}\right)$ (in Volts) at t = 1 sec is_____________.

In the given circuit, the maximum power (in Watts) that can be transferred to the load R${}_L$ is ___________

The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C${}_J$) at a reverse bias (V${}_R$) of 1.25 V is 5 pF, the value of C${}_J$ (in pF) when V${}_R$ = 7.25 V is _________

A MOSFET in saturation has a drain current of $1$ mA for $\mathrm{VDS}=0.5\mathrm{V}.$ If the channel length modulation coefficient is $0.05{\mathrm{V}}^{-1}$, the output resistance (in kΩ) of the MOSFET is _______

For a silicon diode with long P and N regions, the acceptor and donor impurity concentrations are $1\times 10^{17}\mathrm{c}{\mathrm{m}}^3\mathrm{and}1\times 10^{15}\mathrm{c}{\mathrm{m}}^3$ respectively. The lifetimes of electrons in the P-region and holes in the N-region are both 100 μs. The electron and hole diffusion coefficients are $49\mathrm{c}{\mathrm{m}}^3$ and $36\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$ respectively. Assume $\frac{\mathrm{kT}}{\mathrm{q}}=26\mathrm{mV}$, the intrinsic carrier concentration is $1\times 10^{10}\mathrm{c}{\mathrm{m}}^{-3}$ , and $\mathrm{q}=1.6\times 10^{-19}\mathrm{C}.$ When a forward voltage of 208 mV is applied across the diode, the hole current density (in nA / cm²) injected from P region to N region is