ECE107-Midterm1-Solution

ECE107-Midterm1-Solution - ECE 107 Electromagnetism Name...

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ECE 107 - Electromagnetism Spring 2010 Midterm Exam #1 Name _ PID _ #1 Transmission Lines: (do not forget units!) A coaxial cable has the following characteristics: Radius of center conductor: 0.5 mm Radius of outer conductor (inside surface): 3.5 mm Relative dielectric constant: 2.4 (Iossless) Conductivity of conductors: infinite The cable contains no magnetic materials Assume the frequency is 5 GHz 3.5 mm (a) Find the inductance per unit length (1 point) (b) Find the capacitance per unit length (1 point) (c) Find the characteristic impedance (1 point) (d) Find the phase velocity of a wave traveling on this cable (1 point) (e) Find the wavelength of a 5 GHz wave traveling on this cable (1 point)
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(f) Now assume the cable is terminated in a short circuit. A wave is traveling in the +z direction toward the short circuit at z=O, and forms a standing wave. Sketch the magnitude of the voltage and current in the standing wave as a function of z. You do not need to calculate the value at the voltage or current - just sketch the shape of each function.
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