A series RCL circuit has R = 60 Ohm, L = 10.0 mH, and an angular frequency, omeg

Question

A series RCL circuit has R = 60 Ohm, L = 10.0 mH, and an angular frequency, omega = 5000 rad/s. The circuit is connected to an ac source of V_rms = 225 V and the current through the circuit, I_rms = 3.0 A. (a) What is the value of the capacitance, C? (b) What is the phase angle phi? A converging lens is used to project a real image of an object onto a screen. The object and the screen are 100 cm apart. The focal length of the lens is 16 cm. Find two possible locations of the object (i.e., find two object distances) and the corresponding two possible locations of the image (i.e., find two image distances). A diffraction grating has d = 1250 nm. (a) Identify which of the following colors (wavelengths) can be observed in the 2^nd -order diffraction: lambda_1 = 750 nm: lambda_2 = 700 nm: lambda_3 = 650 nm lambda_4 = 615 nm: lambda_5 = 600 nm: lambda_6 = 410 nm: and lambda_7 = 400 nm. Justify your answers with calculations and show your work. (b) Which colors, if any, overlap (i.e., are located at the same position) in the second and third order diffractions? (Show your work). A mixture of two colors of unknown wavelengths, lambda falls perpendicularly on a thin film of gasoline that is formed on a glass plate. For both wavelengths, the refractive index of gasoline is 1.45 and that of the glass plate is 1.50. The minimum non-zero thickness of the film in one spot is 82.76 nm as a result of the destructive interference (elimination of one color). On another spot, the minimum non-zero thicknesses of the film is 100 nm as a result of the destructive interference (elimination of the other color). Identify which two colors are mixed and which color is eliminated in each of the two spots. Use the table below and please show your work.? A negatively charged particle (q_o = -80 mu C m = 4.0 times 10^-16 kg) is released from rest between two plates A and B. The electric potential at plate A is 66 V and the electric potential at plate B is 50 V. (a) From which plate to which plate will the particle move? (b) What is the speed of the particle when it reaches the plate that it moves to? Equation: |q_o| Delta V = 1/2 mv^2

Explanation / Answer

5) impedance Z = Vrms /Irms

= 225/3 = 75 ohm

R^2 + (XL-XC) ^2 = Z^2

60^2 + (0.01*5000-1/(5000C))^2 =75^2

(0.01*5000-1/(5000C)) = sqrt (75^2 - 60^2) = 45

50 - 1/5000C = 45

1/5000C = 5

C = 1/(5000*5)

= 4*10^-5 F

B) phase angle = arccos(60/75)

= 37 degree

  

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