Govt. Exams
Let intensities be I and 4I. Amplitudes are A and 2A. Max intensity = (A + 2A)² = 9A² = 9I
v = √(T/μ) = √(200/(0.1/2)) = √4000 = 63.2 m/s. f = v/(2L) = 63.2/4 = 15.8 Hz... Recalculating: f₁ = √(T/μ)/(2L) where μ = 0.05 kg/m, so f₁ ≈ 44.7 Hz
I_max = (√I₁ + √I₂)² = (√(4I) + √I)² = (2√I + √I)² = (3√I)² = 9I
For successive resonances in a resonance tube, l₂ - l₁ = λ/2, and end correction e ≈ (l₂ - l₁)/2 = λ/4
Comparing with y = Asin(2πft - 2πx/λ), we have 2π/λ = 0.01π, so λ = 200 cm
Maximum particle velocity = ωA = 2πfA = 2πA(v/λ) = 2πAv/λ
The Early effect occurs because increased reverse bias widens the depletion region, reducing the effective base width. This decreases recombination in the base and increases collector current. The Early voltage V_A is inversely proportional to base doping concentration.
Due to lower hole mobility in PMOS (~2-3 times lower than electron mobility in NMOS), the PMOS width must be 2-3 times larger to match switching speeds and minimize inverter delay.
FinFETs employ multiple gates (typically 3 gates) wrapping around a thin silicon fin, providing superior electrostatic control of the channel, reducing short-channel effects and subthreshold swing.
The process transconductance parameter k_n = μ_n × C_ox determines how efficiently the MOSFET converts gate voltage to drain current. Both μ_n and C_ox are independent device parameters.
