Problem 1 - The Wheatstone bridge circuit shown to the left below is governed by the equations provided on the right.

v_a, v_b, v_c, and v_d represent voltages at four different nodes of the bridge circuit, R₁, R₂, R₃, R₄, and R₅, are resistors, and V_in is the source voltage. Assuming that V_in = 12 Volts, R₁ = R₂ = 50 ohms, R₃ = R₄ = 100 ohms, and, R₅ = 1000 ohms, create an m-file which generates the system of four equations in four unknowns (v_a, v_b, v_c  and v_d) to be solved in matrix form and solves them using MATLAB.

Problem 2 - Consider a gas in a piston-cylinder device in which the temperature is held constant. As the volume of the device is changed, the pressure is measured. The experiment is conducted for two different temperatures and the volume and pressure values are reported in the following table.

(a) Create an expanded volume-pressure table with volume measurement starting from 1 m³ with an increment of 0.4 m³ up to 6 m³ and approximate the pressure for each volume using linear and cubic spline interpolation. Show your result by plotting the interpolated values (for both linear and cubic spline) in a single graph.

(Hint: Make a pressure array that contains both sets of data; your volume array will need to be 6x1, and your pressure array will need to be 6x2.)

(b) Create a new column of pressure values at T=400K, using linear interpolation.

(Hint: Use the function interp2 which will allow you two dimensional interpolation)

Problem 3 - Consider the volume-pressure table data at T=300K in Problem 2 (you do not need to consider the pressure column at T=500K). Fit the data using 2^nd  and 4^th  order polynomial. Now with a volume measurement starting from 1 m³ with an increment of 0.2 m³ up to 6 m³, calculate the outputs on these volume measurements using your 2^nd and 4^th order polynomials. Show your result by plotting the actual data (as circles with no line) and curve fitted data (as solid line) in a single graph. Append a comment at the end of your m-file indicating which model is better out of the two.