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BASIC ELECTRICITY OBJ!
01-10: CABAAACCAB
11-20: CACBDCADCA
21-30: DCCDBBCBDC
31-40: CABABCCACC
COMPLETED
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INSTRUCTION: ANSWER FIVE(5) QUESTIONS ONLY
(1ai)
Capacitive reactance is the opposition that a capacitor offers to the flow of alternating current (AC) due to the capacitor’s ability to store and release energy in its electric field. It is inversely proportional to both the frequency of the AC signal and the capacitance.
(1aii)
Inductive reactance is the opposition that an inductor offers to the flow of alternating current due to the inductor’s property of generating a back electromotive force (emf) when the current changes. It is directly proportional to both the frequency of the AC signal and the inductance.
(1bi)
Peak Value of the Voltage(V₀):
The peak value is the amplitude of the sine function:
V₀ = 30 V
(1bii)
RMS Value of the Voltage(Vrms):
RMS value for a sinusoidal voltage is:Vrms = V₀/√2
Vrms = 30/√2 = 30 /1.414 ≈ 21.21V
(1biii)
Angular Frequency(ω):
The angular frequency (ω) is the coefficient of t in the sine function, which is:
ω = 1000π rad/s
(1biv)
Frequency(f):
Frequency is related to angular frequency by:ω = 2πf.
Rearranging for f gives f = ω/2π
f = 1000π/2π = 500Hz
(1bv)
Period(T):
Period is the reciprocal of frequency: T = 1/f
T = 1/500 = 0.002s
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(3ai)
Resistance is the property of a material or device that opposes the flow of electric current through it. It determines how much current will flow for a given voltage applied across the material. It is measured in ohms (Ω).
(3aii)
Inductance is the property of an electrical conductor by which a change in current flowing through it induces an electromotive force (emf) either in the conductor itself or in a nearby conductor. It is measured in Henry (H).
(3bi)
Yellow, Violet, Red, Gold:
-Yellow = 4 (first digit)
-Violet = 7 (second digit)
-Red = 2 (multiplier, 10²)
-Gold = ±5% tolerance
Resistance = 47 × 10² Ω = 4700 Ω = 4.7kΩ
Tolerance = ±5%
(3bii)
Blue, Red, Orange, Silver:
-Blue = 6 (first digit)
-Red = 2 (second digit)
-Orange = 3 (multiplier, 10³)
-Silver = ±10% tolerance
Resistance = 62 × 10³ Ω = 62000 Ω = 62kΩ
Tolerance = ±10%
(3biii)
Brown, Grey, Black, Gold:
-Brown = 1 (first digit)
-Grey = 8 (second digit)
-Black = 0 (multiplier, 10⁰)
-Gold = ±5% tolerance
Resistance = 18 × 10⁰ Ω = 18Ω
Tolerance = ±5%
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(4a)
Ohm’s law states that the current flowing through a conductor is directly proportional to the voltage applied across it, provided the temperature and other physical conditions remain constant. Mathematically, it is expressed as: V = IR
(4b)
(i) They cannot be recharged once exhausted.
(ii) They have a limited lifespan and lose capacity over time.
(iii) They may have a high internal resistance which reduces efficiency.
(iv) They can leak or corrode, causing damage to devices.
(v) The voltage output may drop gradually during use.
(4c)
Given:
-R₁ = 10Ω
-R₂ = 15Ω
-Total emf = 4 × 2 = 8V
-r = 0.2Ω (internal resistance)
-Resistors are in parallel
Equivalent resistance of the parallel combination:
1/Req = (1/R₁ +
1/R₂) = 1/10 + 1/15 = 3+2/30 = 5/30
Req = 30/5 = 6Ω
Total resistance in the circuit (including internal resistance):
R_total = Req + r = 6 + 0.2 = 6.2Ω
Total current from the battery(I_total):
I_total = (emf/R_total) = 8/6.2 = 1.29A
(4ci)
p.d. across each resistor:
V = emf – Ir = 8 – (1.29 × 0.2) = 8 – 0.258 = 7.742V
p.d. across each resistor = 7.742V
(4cii)
Current through each resistor:
For R₁ = 10Ω:
I₁ = V/R₁ = (7.742/10) = 0.774A
For R₂ = 15Ω:
I₂ = V/R₂ = (7.742/15) = 0.516A
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(5ai)
Power is defined as the rate at which work is done or energy is transferred or converted per unit time. The SI unit of power is the watt (W).
(5aii)
Energy is the ability to do work, which means the ability to exert a force causing the displacement of an object. The SI unit of energy is the joule (J).
(5aiii)
Electromotive force (emf) is the energy supplied by a source such as a battery or generator per unit electric charge that passes through it. It is the potential difference across the terminals of the source when no current is flowing. The SI unit of emf is the volt (V).
(5b)
(i) Heating Effect: When electric current flows through a conductor, it generates heat due to the resistance of the material.
(ii) Magnetic Effect: An electric current flowing through a conductor produces a magnetic field around it.
(iii) Chemical Effect: Electric current can cause chemical reactions, such as electrolysis, when passed through an electrolyte.
(5c)
Given:
Effective Inductances of Four Inductors: 2H, 4H, 5H, 10H
(i) Series: For inductors in series, the effective inductance is the sum of the individual inductances:
Leff = L₁ + L₂ + L₃ + L₄
Leff = 2 + 4 + 5 + 10 = 21H
Leff = 21H
(ii) Parallel: For inductors in parallel, the reciprocal of the effective inductance is the sum of the reciprocals of the individual inductances:
Leff = (1/L₁) + (1/L₂) + (1/L₃) + (1/L₄)
Leff = (1/2) + (1/4) + (1/5) + (1/10)
Leff = ((10+5+4+2)/20) = 21/20
Leff = 20/21
Leff = 0.952H
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(6a)
Faraday’s First Law:
Whenever a conductor is placed in a changing magnetic field, an electromotive force (EMF) is induced in the conductor. If the conductor forms a closed circuit, an induced current flows.
Faraday’s Second Law:
The magnitude of the induced EMF is directly proportional to the rate at which the magnetic flux linking the conductor changes. The direction of the induced EMF always opposes the change in magnetic flux that produces it (this is known as Lenz’s Law).
(6b)
A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It typically consists of two coils (primary and secondary) wound around a magnetic core. The transformer operates on the principle of mutual induction, where a changing current in the primary coil induces an EMF in the secondary coil, allowing voltage to be stepped up or stepped down.
(6c)
(i) Copper Losses
(ii) Iron (Core) Losses
(iii) Flux Leakage Losses
(6d)
The efficiency of a transformer is the ratio of the output power to the input power, usually expressed as a percentage. It measures how well the transformer converts input electrical power to output electrical power without losses.
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(7a)
A semiconductor is a material whose electrical conductivity lies between that of a conductor and an insulator. Its conductivity can be controlled and modified by adding impurities or by changing external conditions such as temperature or electric field, making it essential for electronic devices.
(7b)
(i) Silicon (Si)
(ii) Germanium (Ge)
(iii) Gallium Arsenide (GaAs)
(7c)
Doping is the intentional process of adding a small amount of impurity atoms (dopants) to a pure semiconductor material. This process is done to change the semiconductor’s electrical properties by increasing its conductivity, making it more useful for electronic devices.
(7d)
(i) Boron (B)
(ii) Aluminium (Al)
(7e)
(i) Phosphorus (P)
(ii) Arsenic (As)
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