The normal mode frequencies are given by Select one: O a. fn = n/L Ob. fn = nc/2L, n = 1, 2, 3, ... O C. in = n/L Od. kn = n/L
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- 5. A sin wave has the effective value of the Ir,m.s, current =5 mA. find а) Ip b) Ip. c) lavg2. A telecommunication circuit shown in the figure has a parallel inductor and capacitor in series with a resistor. R Eg cos at :CProblem 1: A uniform sphere of mass m and radius r is projected along a rough horizontal surface with a linear velocity vo. The coefficient of kinetic friction between the sphere and the surface is µ. Determine (a) the work done by friction force on the sphere until the time t, at which the sphere will start rolling without sliding, and (b) calculate the total kinetic energy of the sphere at instants t=0 and t=t:{T = Translation +Trotation =mv3 +÷low²}. (c) Is the change in total kinetic energy equal to the work done by the friction force in the time interval [0, t,]? (d) Will there be friction between the sphere and the horizontal surface after the instant t=t,? Explain why. Note: Do NOT use D'Alembert's Principle.
- 2. A square copper frame has sides of length b. A very long thin solenoid goes through the frame as shown. The solenoid has N tums in a total length H and radius a. Assume that > > 2a so the solenoid goes through the frame. The solenoid has an AC current given by I(t) = 1, sin(at) with cow counted as positive. The angular frequency w is constant. a. Write an expression for the magnetic flux through the square frame as a function of time. Hint: what is the magnetic field inside and outside a long solenoid? b. Determine the EMF induced in the frame as a function of time. Please use Faraday's Law with the minus sign. ފޕފ O 2a head on view b c. What is the amplitude of the induced EMF? The amplitude of a sinusoidal function is the maximum deviation of the function from the average value. Hint: what is the largest value that cosine or sine can have during a cyde? d. What is the induced EMF as a function of time if the square frame was small enough to fit entirely inside the solenoid (> <2a)…E H A coaxial capacitor with inner radius 5 mm, outer radius 6 mm and length 500 mm has a dielectric for which e,=6.7 and an applied voltage 250 sin 377t (V). Determine the displacement current ip and compare with the conduction current i̟.Derive an expression for the wave equation in free space. Intrinsic impedance for free space =120π or 377Ω, Justify?
- What is the magnitude of the impedance Z between nodes A and B with a resistance of R, a capacitance of C, and an inductance of L with the following values: w = 3600 rad/s, R = 50 M, L = 2.0 × 10-8 H, C = 12 μF. A ww reler BØ = 20 mm m₁ = 476 Wdg/m n₂ = 300 Wdg f = 10.7 kHz = 10.7 x 10³ Hz Ho,theoretical = 4 x 10-7 N/A² 1.26 x 10-6 N/A² Calculate the cross-sectional area of the induction coil: A = πr² = π (× 10-³)² = Write down the slope of the line: slope = [m] =3.81 • Using the relation emf = μoAn₁n₂ (2πf)1, calculate the experimental value for vacuum permeability: slope Mo,experimental Anin₂ (2f) Calculate the error percentage: error % = Ho.theoretical Ho,experimentai Mo,theoretical x 100% =6. The response of a band rejected filter is characterized in — — — — — A A ¢ ) 0 B 2 i i it