For the function; T=x2 + 4 xy + 2 yz3 and the points a=(0, 0, 0), b= (1, 1, 1), check the fundamental theorem for gradients April 11, 2016 Read More »
A particle of mass 3 units moves in a force field depending on time t given by; F=12t2i +(6t – 3)j -3tk .If its position vactor at time t=0 seconds is given by; ro= 2i + j -2 k and its initial velocity at this instant given by; Vo=4i +5 j + 3k Detemine Its velocity and position at any time(t).(4 marks) Torque and angular momentum about the origin for the particle at time(t) April 11, 2016 Read More »
Define a conservative force field.( 1 mark) (ii)A conservative force may be expressed as: ?(?-F )=- ?(?-? ?(?-V )) Show that for such a force, ??×F = 0 (4 marks) (iii)Show that a force field defined by; F=(6xyz + z2)i + 3 x2yz j + (3 x2y + 2xz)k is a conservative force field. (3 marks April 11, 2016 Read More »
A 6H inductor is placed in series with a 30O resistor, an e.m.f of 8 V suddenly being applied to the combination. At 0.60 seconds after contact is made. Calculate: (i) The rate at which energy is delivered by the battery. (ii) The rate at which Joule heating appears in the resistor. (iii) The rate at which energy is stored in the inductor. April 11, 2016 Read More »
A coil has an inductance of 0.4 H and a resistance of 20O. It is connected to a 240V, 50 Hz supply. Determine; (i) The reactance of the coil. (ii) The impedance of the circuit. (iii) The maximum current through the coil. April 11, 2016 Read More »
A long solenoid of radius 3 cm and 5000 turns per unit length carries a varying current, i, given by i=4 sin21t where t is time in seconds. Calculate the magnitude of the tangential electric field on a loop of radius 4cm after 10 seconds. Assume the coil and solenoid are concentric. April 11, 2016 Read More »
A conducting cylinder of radius RO and length L, and carrying charge -2q, is surrounded by a conducting cylindrical shell of radius R and charge +5q. Use Gauss’s law to find: (a) The electric field strength at point r outside the conducting shell. (b) The charge on the inside and outside surfaces of the conducting shell. (c) The electric field strength in the region between the cylinders. April 11, 2016 Read More »
) An inductor and a capacitor are connected one at a time to a variable frequency power source. State how, and explain in non-mathematical terms why, the current through the circuit varies as the frequency varies April 11, 2016 Read More »
A coil of self inductance 0.8H and a resistor resistance 84O are connected to a 240Vp, 50Hz power line. (i) Calculate the phase angle between the voltage across the inductor and input voltage. (ii) Calculate the current flowing in the circuit. April 11, 2016 Read More »