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Find the area bounded by the curves x=y²,x+y-2=0
Using Green's theorem,evaluate ∮c(x+y)dx+ x²dy, C is the triangle
with vertices at (0,0). (2,0) and (2, 4), taken in that order.
Find the work done by a force F= -xyi+y²j + zk in moving a particle over the circular path x² + y² = 4, z = 0 from (2,0,0) to (0,2,0)
Find the constants a, b, c if the vector F = (2x+3y+az)i + (bx+2y+3z)j + (2x+cy+3z)k is conservative.
An air filled rectangular waveguide has TE10 mode cut off frequency of 8Ghz. The signal frequency is 15 GHz and the ratio a/b is 2. If the waveguide is now filled with perplexed of relative permittivity 2.5 , find the guide wavelength of the signal.
Given the following parameters Vin = 14 V, R1 = 24 kΩ, R2 = 12 kΩ, R3 = 6 kΩ,
R4 = 3 kΩ and a feedback resistor of 10 kΩ. Calculate the output voltage V0. (9)
A combinational circuit has four inputs (A,B,C,D), which represent a binarycoded-decimal digit. The
circuit has two groups of four outputs - S,T,U,V(MSB digit) and W,X,Y,Z.(LSB digit)Each group
represents a BCD digit. The output digits represent a decimal number which is five times the input
number. Illustrate the minimum expression for all the outputs?
This problem illustrates both the structure of a diatomic molecule and the large disparity between changes in rotational, vibrational, and electronic energy levels. It also illustrates the formation of a band head, the abrupt end of a spectroscopic band. The following data for I2 are available from the NIST website:
(a) Construct an energy-level diagram for the ground electronic state. Consider only the first 10 rotational levels within the first two vibrational levels. Label the ordinate in cm−1 and indicate the total degeneracy of each individual rotational energy level on the diagram. 242
(b) Determine the energies (in cm−1 ) of the 10 purely rotational transitions for the v = 0 energy level within the ground electronic state and plot them on a second energy-level diagram. Draw a vertical line representing v = 0, J = 10 → 9 on the diagram from part (a).
