GATE IN 2013 Question Paper (10-Feb-2013) (Shift 2)

Measurement of optical absorption of a solution is disturbed by the additional stray light falling at the photo-detector. For estimation of the error caused by stray light the following data could be obtained from controlled experiments.

Photo-detector output without solution and without stray light is 500 μW.

Photo-detector output without solution and with stray light is 600 μW.

Photo-detector output with solution and with stray light is 200 μW.

The percent error in computing absorption coefficient due to stray light is

Two ammeters A₁ and A₂ measure the same current and provide readings I₁ and I₂, respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variables of standard deviations σ₁ and σ₂ , respectively. The value of the current is computed as :

I = μI₁ + (1 - μ)I₂

The value of μ which gives the lowest standard deviation of I is

A tungsten wire used in a constant current hot wire anemometer has the following parameters :

Resistance at 0° C is 10Ω, Surface area is 10⁻⁴ m² , Linear temperature coefficient of resistance of the tungsten wire is 4.8 × 10⁻³ /°C, Convective heat transfer coefficient is 25.2W / m² /°C, flowing air temperature is 30°C, wire current is 100 mA, mass-specific heat product is 2.5 × 10⁻⁵ J /°C

A piezo-electric force sensor, connected by a cable to a voltage amplifier, has the following parameters :

Crystal properties : Stiffness 10⁹ N/m, Damping ratio 0.01, Natural frequency 10⁵ rad/s, Force-to-Charge sensitivity 10⁻⁹ C/N, Capacitance 10⁻⁹ F with its loss angle assumed negligible

Cable properties : Capacitance 2 × 10⁻⁹ F with its resistance assumed negligible

Amplifier properties : Input impedance 1 MΩ, Bandwidth 1MHz , Gain 3

Consider a plant with the transfer function G(s)=1 / (s +1)³. Let Kᵤ and Tᵤ be the ultimate gain and ultimate period corresponding to the frequency response based closed loop Ziegler-Nichols cycling method, respectively. The Ziegler-Nichols tuning rule for a P-controller is given as : K = 0.5 Kᵤ