Practice Problems in Electrical and Mechanical Engineering

Section A (Electrical)

QA1 (a) A battery has an open-circuit voltage of 12 V and a full-load rated current of 1 A. When a load resistance R is connected across it drawing the full rated current of the battery, the load voltage is found to be 11 V. Determine the internal resistance of the battery and its voltage regulation.

(b) Determine the resistance, at room temperature, of a copper wire having a diameter of 2.0 mm and a length of 500 m. You may assume that the resistivity of copper at room temperature is 1.72x10.

(c) The circuit in Figure Q1 is a potential divider. Use Microsoft Excel, or any similar software, to plot the variation of the output voltage with variation in R2 over a suitable range.

Making any reasonable assumptions and modifications, explain how this circuit may be used as a darkness detector which can turn a mains-powered lamp automatically during darkness.

(a) Reduce the circuit to the left of terminals a-b to its Norton’s equivalent circuit.

(b) Reduce the circuit to the right of terminals a-b to its Thevenin's equivalent circuit.

(c) A load resistance R_{L =}10 is now connected between terminals a-b. Using parts (a) and (b) and the superposition principle, determine the current in the load resistance R_L.

(d) Calculate the power dissipated in the load resistance and if the load remains connected for 5 minutes, calculate the electrical energy converted to heat in the load.

(e) Determine the value of the load resistance, which when connected between terminals a and b, will draw maximum power from the circuit and use Microsoft Excel, or any similar software, to plot a graph showing the variation in the power delivered to the load for a suitable range of the load resistance and Comment on your graph.

QA3 A series RLC circuit is connected across an AC voltage source of 230 V (rms) 50 Hz. Given that the resistance R is 30 ohms, the inductance L=100 mH, and C = 250 uF :

(a) Calculate the impedance of the circuit and sketch the Z-triangle.

(b) Determine the magnitude and phase of the circuit current.

(c) Calculate the voltages across R, L and C and sketch a phasor diagram showing the circuit current and voltages.

(d) Calculate the circuit apparent power, true power and reactive power and sketch a labelled power triangle.

(e) Find the supply frequency that will allow the circuit to draw maximum current from the AC source. Explain, briefly, the significance of this frequency.

QA1 (a) Battery Resistance and Voltage Regulation

QB1 The link shown in figure QB1 is subjected to the forces F₁ = 500 N and F₂ =350 N.

(a) Determine the magnitude of the resultant force. (5 marks)

(b) Determine the direction of the resultant force. (3 marks)

(c) Express both forces F₁, F₂, and the resultant force in vectorial notation (2 marks)

QB2.1 Figure QB2a shows the graph of the velocity trend with time, associated with a car in rectilinear motion.

(a) Determine the distance travelled after 50 s, and the distance travelled after 90 s.

(b) Determine the average velocity of the car. (3 marks)

(c) Determine the acceleration at the time instants t = 40 s and t = 70 s.

QB2.2 A ball is launched against a wall at an initial velocit = v₀ 25 m/s with the inclination angle indicated in figure QB2b. The distance between the wall and the launch position is 22 m.

(a) Determine the total time between the instant at which the ball was launched and the instant at which the ball hits the wall.

(b) Determine the vertical distance (i.e. the height difference) from the launch position, at which the ball will hit the wall.

(c) Determine the horizontal and vertical components of the velocity at the time instant the ball hits the wall.

(d) Explain if, by the time the ball hits the wall, it has already passed from the point of maximum height of the trajectory, and why. 

QB3.1 Figure QB3a shows a beam supported by two pin constraints at its ends, A and B, subjected to distributed loads as indicated.

(a) Sketch the free body diagram for this system, with clear indication of the reaction forces

(b) Determine magnitude and position of the equivalent concentrated loads corresponding to the distributed loads in each relative part of the beam, namely from 0 to 0.4 m (distance from A), from 0.4 m to 1.2 m, and from 1.2 m to 2 m.

(c) Determine the reaction forces in A and B, by solving the associated system of static equilibrium equations.

(d) Determine the internal forces at the section distant 1 m from A.

QB3.2 Consider now the beam loaded as shown in figure QB3b, with reaction forces already provided. Determine the equations of the shear load and moment T(x), M(x) along the beam length, and draw the relative diagrams.