5. Consider a dielectric sphere of radius 10 cm and dielectric constant of 1.2 and conductivity of 10 S/m. At time t=0, lightning strike this sphere and deposits a uniform charge of ImC in to the sphere. (a) What is the electric field intensity inside and outside this sphere for t> 0? What is the current density n the sphere? (b) Calculate the change in the electrostatic energy stored in the sphere as the charge diminishes to 1% of its initial value? (c) Determine the electrostatic energy stored in the sphere outside the sphere. Does this energy change with time?

2. Calculate the following values for an ideal transformer when Vp = 10oy,Vs = 400V and R, = 3k.(20 marks) a ip = b.Is = C.Apparent Power Secondary = d.Apparent Power Primary = e.Turns Ratio =

3. The Insulated Power Cable Engineers Association (ICEA) recommends the following approximated formula for the damage curve of cables (copper conductor): \left[\frac{T}{A}\right]^{2} t=0.0297 \log \left[\frac{T_{2}+234}{T_{1}+234}\right] where: I = current in Amps A = conductor’s area in CICULAR MILS (CM) t = damage time T1 = initial temperature in C T2 = damage (final) temperature in C Demonstrate that this equation is equivalent to the equation derived in class using metric units: I^{2} t=\frac{C D A^{2}}{\rho_{0} \alpha_{0}} \ln \left[\frac{1+\alpha_{0}\left(T_{d}-T_{0}\right)}{1+\alpha_{0}\left(T_{i}-T_{0}\right)}\right]

(a) Refer to Figure Q6(a). Indicate which of the 9V 100mA lamps are bright, dim oroff. Give reasons to support your answer.[6 Marks] (b) Sketch the current, I, versus voltage, V, characteristics curves for silicon andgermanium diodes. Conduction does not start until the forward biased voltage VFis about 0.6V for silicon and 0.1V for germanium. Also assume that the reversevoltage, VR, can be of value of 1000V for both diodes.[8 Marks] (c) In the circuit of Figure Q6(b), hFE = 100 for a bipolar junction transistor (BJT). Calculate the value of RB for the lamp current Ic to be 60MA. Assume the transistor's not saturated and that VBE = 0.6V.[8 Marks] (d) If the lamp shown in Figure Q6(b) has resistance RL100ohms, would the transistor be saturated?[3 Marks]

Schematic of drag force measurement system utilized in sphere drag experiment:2. Label the functional instrument groups 1-3 in the diagram using our generic measurement system terminology from class (or F&B 1.2).а. b.Considering the system as four equivalent linear instruments connected in series: Instrument 1, consisting of the sphere/stinger/strut, balance, load cell and bridge circuit, and having a composite sensitivity K. of 4.0 mV/N and composite DC zero offset O, of 27 mV; Instrument 2, the amplifier, with a gain G, of 20DB and O, = -25 mV Instrument 3, the lowpass filter, with unity gain G. and O, = 9.0 mV; Instrument 4, the voltmeter, with K, = 1.03 (what units??) and O, = -11mV; i.Draw a block diagram for the 4-instrument system, labeling the intermediatesignals between instruments as x.y, and z respectively, with F the input and Wthe output. Construct an analytical expression for each Instrument's response function. iii.Derive the system response function. Determine the system sensitivity - evaluate the sensitivity at 1.0 N input force. v.Determine the force being measured if the voltmeter reads 0.72 volt.

The rectifier in the figure below has a purely resistive load of R = 10 2, determine: (a) the efficiency (b) the form factor (c) the ripple factor

4. A 40 kVA, 2000/200 V single-phase transformer has a core loss of 600W at rated voltage and a copper loss of 500W at rated current. Calculate the efficiency at i) full load with unity power factor, half load with 0.85 power factor lagging.

(4) The figure below shows a four-lead bridge circuit commonly found in oil & gas field instruments; R.is the resistance of the leads or cables connecting the sensor to the bridge circuit. Show that ETh = Vs(Ro/R3)aT, i.e., the bridge output voltage is unaffected by changes in Rc.

(a) Let a 100-V sinusoidal ac source be connected to aseries combination of a 3-2 resistor, an 8-Q inductor, anda 4-0 сараcitor. Draw the circuit diagram and the phasor diagram.(i) Compute the series impedance.(ii) Determine the current I delivered by the source.(iii) Is the current lagging or leading the source voltage,(iv) calculate the power factor. Calculate the power triangle of the circuit. (b) |A single phase load is operating at lagging power factor and draws 10 A from the ac supply. A device is proposed to "increase the efficiency" of the motor. During a demonstration the device is placed in parallel with the load and the current from the supply drop to 8 A. When two of these devices are placed in parallel the current drop further to 6 A. What simple device will cause this drop in current? Discuss the advantages of this device. Is the efficiency of the load increased by the device?

3. A long grounded conducting cylinder of radius b is placed along the z axis in an initially uniform electric field Eo = Eo ax. Determine the potential distri- bution and electric field intensity outside the cylinder. Show that the electric field intensity at the surface of the cylinder may be twice as high as that in the distance, which may cause a local breakdown or corona. See St. Elmo's fire.