1. In the following figl., let R=200 2 ,C=15.OuF,L=230mH, fa = 60.0Hz , and Em = 36.OV . a) What is the impedance Z of the circuit? b)what is the current amplitude I? c) What should be the frequency fa , if the circuit is in resonance and other parameters remain unchanged? (15points) 800 A transverse wave travelling along a horizontal string, a positive displacement y means upward, x measured in meters and t in seconds( 16marks) y(x, t) = (4.00mm) sin(2xx - 400nt + 0.7) (a) What is the amplitude of the wave? Answer [ (b) What is the wavelength? Answer [ (c) What is the frequency? Answer [ (d) What is the speed of the wave? The wave travels to the positive or negative direction of x axis? Answer [ (f) What is the speed of the point at x=0 when t=0s? Is it moving upward or downward? Answer [2. Draw a figure and Describe the basic working principle of ideal transformer. (illustrative figure needed, not more than 200words) (15ps) 3. A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field, as indicated in Fig2. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the emf induced in the coil is given (as a function of time t) by E = 2pfaNab sin(2p.ft) = E, sin(2pft) This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with E. = 150 when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T? (15ps) Sliding contacts - BXXXXXX XXXX XXXXXXX X4. Charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R. (a) Show that, at a distance r R. (15ps) 5. Show that the magnetic field at point P of a current i in a long straight wire is B= mi 2pd here d is the distance from point P to the wire. (15ps)6. Show that the capacitance of a spherical capacitor with concentric spherical plates of radii a and b has capacitance is (15ps) C = 4pejab b - a 7. Describe, in your own words, what is self-induction of a inductor, not more than 200 words.(10ps)