Electrical Technology Exam

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### Exam Instructions - **Date:** 11 February 2026 - **Time Allowed:** 3 Hours - **Instructions:** Answer all questions. Marks are indicated in brackets. Use diagrams where appropriate. Calculators are permitted. - **Total Marks:** 100 ### Section A: Multiple Choice (20 marks) Answer all questions by circling the correct option. 1. What is the SI unit of electrical resistance? a) Volt b) Ampere c) **Ohm** d) Watt (1 mark) 2. In a series circuit, the total resistance is: a) **The sum of individual resistances** b) The reciprocal of the sum of reciprocals c) The product of individual resistances d) The average of individual resistances (1 mark) 3. Which component stores electrical energy in an electrostatic field? a) Resistor b) Inductor c) **Capacitor** d) Diode (1 mark) 4. The power dissipated in a resistor is given by: a) P = V/I b) P = I²R c) P = V²/R d) **Both b and c** (Note: $P = IV$, and by Ohm's Law $V=IR$, so $P = I(IR) = I^2R$ and $P = (V/R)V = V^2/R$) (1 mark) 5. What does AC stand for in electrical terms? a) **Alternating Current** b) Active Current c) Amplified Current d) Analog Current (1 mark) 6. In a parallel circuit, the total current is: a) **The sum of individual currents** b) The reciprocal of the sum of reciprocals c) The product of individual currents d) The average of individual currents (1 mark) 7. Which law states that the induced EMF is proportional to the rate of change of magnetic flux? a) Ohm's Law b) **Faraday's Law** c) Kirchhoff's Law d) Coulomb's Law (1 mark) 8. The efficiency of a transformer is highest when: a) Load is maximum b) Load is minimum c) There are no losses d) **Copper losses equal iron losses** (Condition for maximum efficiency) (1 mark) 9. What is the function of a fuse in an electrical circuit? a) To store energy b) To regulate voltage c) **To protect against overcurrent** d) To convert AC to DC (1 mark) 10. In a three-phase system, the phase difference between voltages is: a) 90° b) **120°** c) 180° d) 0° (1 mark) ### Section B: Short Answer Questions (40 marks) Answer all questions in the spaces provided. 1. **Define electrical conductivity and give its SI unit.** (2 marks) * **Electrical Conductivity:** A measure of a material's ability to conduct electric current. It is the reciprocal of resistivity. * **SI Unit:** Siemens per meter (S/m) or mho per meter (℧/m). 2. **Explain the difference between a conductor and an insulator with examples.** (3 marks) * **Conductor:** A material that allows electric current to flow easily through it due due to the presence of free electrons. * *Examples:* Copper, Aluminum, Silver. * **Insulator:** A material that resists the flow of electric current due to the absence of free electrons. * *Examples:* Rubber, Plastic, Glass. 3. **Calculate the total resistance of a series circuit with resistors of 5 Ω, 10 Ω, and 15 Ω.** (2 marks) * For a series circuit, total resistance $R_T = R_1 + R_2 + R_3$. * $R_T = 5 \Omega + 10 \Omega + 15 \Omega = 30 \Omega$. * **Answer:** $30 \Omega$. 4. **Draw a simple circuit diagram showing a battery, a switch, and a bulb in series. Label the components.** (3 marks) * (Diagram would show a battery symbol, followed by a switch symbol, followed by a bulb symbol, all connected in a closed loop. Labels for each component would be present.) 5. **State Ohm's Law and derive the formula for power using it.** (3 marks) * **Ohm's Law:** States that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them, provided the temperature and other physical conditions remain constant. Mathematically, $V = IR$. * **Power Derivation:** * Electrical Power $P = VI$. * Substitute $V = IR$ from Ohm's Law: $P = (IR)I = I^2R$. * Substitute $I = V/R$ from Ohm's Law: $P = V(V/R) = V^2/R$. 6. **Describe the working principle of a transformer. Include the roles of primary and secondary coils.** (4 marks) * **Working Principle:** A transformer works on the principle of mutual induction. When an alternating current flows through the primary coil, it produces a continuously changing magnetic flux. This changing flux links with the secondary coil and induces an electromotive force (EMF) in it. * **Primary Coil:** Connected to the AC supply, it draws current and creates the varying magnetic flux. * **Secondary Coil:** Not electrically connected to the primary, but magnetically coupled. The induced EMF in this coil provides the output voltage and current. 7. **A 220 V, 100 W bulb is connected to a 220 V supply. Calculate the current drawn and the resistance of the bulb.** (3 marks) * **Current drawn (I):** * $P = VI \Rightarrow I = P/V = 100 \text{ W} / 220 \text{ V} \approx 0.45 \text{ A}$. * **Resistance of the bulb (R):** * $R = V/I = 220 \text{ V} / 0.45 \text{ A} \approx 488.89 \Omega$. * Alternatively, $R = V^2/P = (220 \text{ V})^2 / 100 \text{ W} = 48400 / 100 = 484 \Omega$. 8. **Explain the term "electromagnetic induction" with a practical example.** (3 marks) * **Electromagnetic Induction:** The process by which an electromotive force (EMF) is induced across an electrical conductor in a changing magnetic field. This is the fundamental principle behind generators, transformers, and inductors. * **Practical Example:** A **generator**. When a coil of wire rotates within a magnetic field (or a magnet rotates near a coil), the magnetic flux linking the coil changes, inducing a current and voltage in the coil, thus generating electricity. 9. **What are the advantages of using three-phase over single-phase power systems?** (3 marks) * More efficient transmission of power for the same amount of conductor material. * Constant power output, leading to smoother operation of motors and less vibration. * Self-starting capability for three-phase induction motors without auxiliary windings. * Can provide both single-phase and three-phase loads from the same system. 10. **Discuss the safety precautions to be taken when working with high-voltage electrical equipment.** (3 marks) * Always ensure equipment is de-energized and locked out before working on it. * Use appropriate Personal Protective Equipment (PPE) such as insulated gloves, safety glasses, and flame-retardant clothing. * Never work alone. * Use insulated tools. * Be aware of minimum approach distances to live parts. * Follow manufacturer's instructions and safety regulations. ### Section C: Long Answer Questions (40 marks) Answer any two questions. 1. a) **Explain the construction and working of a DC motor. Include a diagram.** (10 marks) * **Construction:** * **Stator:** Stationary part, housing field windings (electromagnets) or permanent magnets that produce the magnetic field. * **Rotor (Armature):** Rotating part, consisting of a core with armature windings and a commutator. * **Commutator:** A split-ring device that reverses the direction of current in the armature windings every half rotation, ensuring continuous unidirectional torque. * **Brushes:** Stationary carbon contacts that press against the commutator to supply current to the armature windings. * **Working Principle:** * When current flows through the armature windings, they become electromagnets. * According to the Lorentz force law ($F = BIL$), a force is exerted on the current-carrying conductors in the magnetic field. * The forces on the sides of the armature coil are in opposite directions, creating a torque that causes the armature to rotate. * The commutator ensures that the direction of current in the armature conductors under each pole is always such that the torque produced is continuous and in the same direction, leading to continuous rotation. * (Diagram would show a basic DC motor with stator, rotor, commutator, and brushes labeled, along with magnetic field lines and current direction.) b) **Calculate the torque produced by a DC motor with armature current of 5 A, flux per pole of 0.02 Wb, and 4 poles.** (5 marks) * Formula for torque in a DC motor is $T = (PZ\phi I_a) / (2\pi A)$, where $P$ is number of poles, $Z$ is total number of armature conductors, $\phi$ is flux per pole, $I_a$ is armature current, and $A$ is number of parallel paths. * *Note: To calculate torque accurately, the number of armature conductors (Z) and the number of parallel paths (A) are also needed. Assuming a simplified context or missing information, a direct calculation isn't possible without these. If this were an exam, a student would state this assumption or ask for more data.* * *If we were to assume a constant $K$ related to the motor's design:* $T = K \phi I_a$. * *Given the provided information, this question might be testing the understanding of the factors influencing torque rather than a direct calculation.* * *For a typical scenario, if it's a 4-pole lap wound motor, A=P=4. If wave wound, A=2.* Let's assume some typical values for Z. * *Without Z and A, a definitive numerical answer cannot be given. The question might be flawed or expecting a conceptual answer about how these values relate.* 2. a) **Describe the types of faults in a three-phase transmission line and their effects.** (8 marks) * **Types of Faults:** * **Symmetrical Faults:** All three phases are short-circuited to each other or to ground. Occur rarely (2-5% of faults). * *Example:* Three-phase short circuit (LLL), Three-phase short circuit to ground (LLLG). * *Effects:* High fault currents, severe voltage dips on all phases, significant mechanical stress on equipment. * **Unsymmetrical Faults:** Involve only one or two phases, or one or two phases to ground. More common (95-98% of faults). * *Examples:* Single Line-to-Ground (LG), Line-to-Line (LL), Double Line-to-Ground (LLG). * *Effects:* * **LG:** Most common. High current in the faulted phase and ground, voltage depression on the faulted phase, phase shift in healthy phases. * **LL:** Two phases shorted. High current in the two faulted phases, voltage dip between them. * **LLG:** Two phases shorted to ground. High current in two faulted phases and ground, severe voltage dips. * **General Effects of Faults:** * Sudden increase in current. * Sudden decrease in voltage. * Damage to equipment due to excessive current and thermal stress. * Interruption of power supply. * Instability in the power system. * Fire hazards. b) **Explain the principle of operation of a circuit breaker.** (7 marks) * **Principle of Operation:** A circuit breaker is an automatically operated electrical switch designed to protect an electrical circuit from damage caused by overcurrent or short circuit. Its basic function is to detect a fault condition and interrupt current flow. * **Detection:** It uses various mechanisms (thermal, magnetic, or electronic relays) to detect abnormal current levels. * **Thermal Trip:** An overcurrent heats a bimetallic strip, causing it to bend and trip the mechanism. (For sustained overloads) * **Magnetic Trip:** A large short-circuit current creates a strong magnetic field that pulls an armature, tripping the mechanism instantaneously. (For sudden, high short-circuits) * **Electronic Trip:** Microprocessor-based relays monitor current and voltage, providing precise and configurable fault detection. * **Interruption:** Once a fault is detected, a spring-loaded mechanism quickly separates the electrical contacts, creating an arc. * **Arc Extinction:** The arc is then extinguished using various methods depending on the type of circuit breaker (e.g., oil, air blast, SF6 gas, vacuum). This prevents further current flow and protects the circuit. * **Resetting:** After the fault is cleared, the circuit breaker can be manually or automatically reset to restore power. 3. a) **Derive the formula for the capacitance of a parallel plate capacitor.** (6 marks) * Consider a parallel plate capacitor with two plates of area $A$, separated by a distance $d$, and a dielectric material with permittivity $\epsilon$ between them. * **1. Electric Field (E):** For a uniform electric field between the plates, $E = \sigma / \epsilon$, where $\sigma$ is the surface charge density. * **2. Surface Charge Density ($\sigma$):** $\sigma = Q / A$, where $Q$ is the charge on one plate. So, $E = Q / (\epsilon A)$. * **3. Voltage (V):** The potential difference (voltage) across the plates is $V = Ed$. * **4. Substitute E into V:** $V = (Q / (\epsilon A)) \times d = Qd / (\epsilon A)$. * **5. Capacitance (C):** By definition, capacitance $C = Q / V$. * **6. Substitute V into C:** $C = Q / (Qd / (\epsilon A)) = Q \times (\epsilon A / Qd) = \epsilon A / d$. * **Formula:** $C = \epsilon A / d$. * For vacuum or air, $\epsilon = \epsilon_0$, so $C = \epsilon_0 A / d$. b) **A capacitor of 10 μF is charged to 100 V. Calculate the energy stored in it.** (4 marks) * Given: Capacitance $C = 10 \mu F = 10 \times 10^{-6} F$. * Voltage $V = 100 \text{ V}$. * Formula for energy stored in a capacitor: $E = \frac{1}{2} CV^2$. * $E = \frac{1}{2} \times (10 \times 10^{-6} \text{ F}) \times (100 \text{ V})^2$. * $E = \frac{1}{2} \times 10 \times 10^{-6} \times 10000$. * $E = \frac{1}{2} \times 10 \times 10^{-6} \times 10^4$. * $E = 5 \times 10^{-2} \text{ J} = 0.05 \text{ J}$. * **Answer:** The energy stored in the capacitor is 0.05 Joules. c) **Discuss the applications of capacitors in electrical circuits.** (5 marks) * **Energy Storage:** Store electrical energy in an electric field (e.g., camera flashes, defibrillators). * **Filtering:** Block DC current while allowing AC current to pass (e.g., in power supplies to smooth out ripple voltage, in audio crossovers). * **Timing Circuits:** Used in conjunction with resistors to create time delays (RC circuits). * **Coupling/Decoupling:** Couple AC signals between stages of an amplifier while blocking DC, or decouple power supply noise from sensitive circuits. * **Motor Starting:** Provide a phase shift for starting single-phase AC motors (start capacitors). * **Power Factor Correction:** Improve the power factor of inductive loads in AC power systems. * **Frequency Tuning:** Used in resonant circuits for radio and TV tuning.