1. For the circuit shown below, the current leads the sinusoidal emf by 14.0°.
   (a) Use the phasor method to determine the unknown resistance R.
   (b) Use complex methods to determine the Z_equivalent of the circuit.
   
   

2. A 60.0 Hz sinusoidal voltage is feed, via an ideal transformer, into the odd centre-tapped rectifying circuit below. For the transformer, N_in::N_out = 250::250. The diodes are silicon. The peak value of the input voltage is 4.20 Volts.
   (a) Give an accurate sketch of the output voltage. Be sure to indicate maximum and minimum values on your sketch.
   (b) Determine V_DC. Determine the RMS value of the output. Find the RMS value of the AC part of the wave.
   (c) Give an accurate sketch of the AC part of output voltage. Be sure to indicate maximum and minimum values, as well as the DC offset, on your sketch.
   (d) The output voltage is feed into another ideal transformer, N_in::N_out = 150::300. For the new output voltage, determine V_DC.
   (e) Give an accurate sketch of the output voltage. Be sure to indicate maximum and minimum values, as well as the DC offset, on your sketch. (Hint - it doesn't just look like a bigger version of (b). Review how transformers work.)
   
   

3. A flat coil is wound so that it contains a very large uniform number of turns per unit distance, n, along its radius from a to b as shown in the diagram below. Determine the field at the centre of the coil, due to the coil, by direct integration. The wire carries a current I. Hint - consider a ring of thickness dr.
   
   

4. Consider a thin spherical shell of radius R carrying a charge Q. Around the shell, are two dielectric shells of thickness a and b respectively. Finally there is a last spherical shell carrying a charge -Q. The relative permittivity of the first dielectric shell is ε_a, and ε_b for the second. Note ε_a > ε_b. (Information on spherical cooordinates is in a math appendix at the back of Duffin)
   (a) Use Gauss' Law to find D, E, and P everywhere.
   (b) Sketch E as a function of radial distance.
   (c) Determine Σ_p and ρ_p for the dielectrics.
   
   

5. A dipole is perpendicular to an infinite conducting plate. Use the Method of Images to get the induced charge distribution Σ on the surface of the plate as a function of x - assume a >> L and keep only terms to first order in L.
   
   

6. For the circuit below, find the current through each resistor. The AC sources are V₁ = 4sin(200t) and V₂ = 3.5sin(400t). The AC and DC sources have no internal resistance.
   
   

7. A thick conducting cylindrical shell has an inner core and an outer sheath made of a magnetic material which has a relative permeability μ_r. The conducting shell carries a current density j(r) = Ae^-Kr/r and is directed out of the paper.
   (a) Determine H, B, and M for all r, where r is the radial distance from the centre of the cylinder. Be sure to indicate the direction of these fields.
   (b) Determine J_SM and J_M for the magnetic materials. (Information on cylindrical coordinates is in a math appendix at the back of Duffin.)
   
   

Questions? mike.coombes@kpu.ca