Lesson Notes By Weeks and Term v3 - Senior Secondary 2
Alternating current circuits
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Alternating current circuits
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Subject: Basic Electronics
Class: Senior Secondary 2
Term: 1st Term
Week: 3
Theme: Electronic Components And Circuits
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Define the terms:- capacitive reactance- in ductive reactance- Impedance. Explain RL and RC Explain RLC circuit. Calculate in ductive and capacitive reactance (XL and XC). Explain series and parallel resonance Calculate series and parallel resonance.
Alternating Current (AC) is an electric current whose magnitude and direction vary cyclically, typically in a sinusoidal pattern. Unlike Direct Current (DC), which flows in one direction, AC periodically reverses direction. This characteristic allows for efficient transmission of electricity over long distances using transformers, which only work with changing magnetic fields produced by A
C. Definition: Inductive reactance ($X_L$) is the opposition offered by an inductor to the flow of alternating current. It arises from the inductor's property of opposing changes in current by inducing a back electromotive force (EMF).
Explanation: When AC flows through an inductor, the continually changing current creates a continually changing magnetic field. This changing magnetic field induces a voltage (back EMF) across the inductor that opposes the change in current (Lenz's Law). The faster the current changes (higher frequency) or the larger the inductance, the greater this opposition.
Formula: $X_L = 2 \pi f L$ Where: $X_L$ is the inductive reactance in Ohms ($\Omega$) $\pi$ (pi) is approximately 3.142 $f$ is the frequency of the AC in Hertz (Hz) $L$ is the inductance of the inductor in Henrys (H)
Key Characteristics: $X_L$ is directly proportional to frequency ($f$) and inductance ($L$). At DC ($f=0$), $X_L = 0$, meaning an inductor acts as a short circuit (ideally). In a purely inductive circuit, the current lags the voltage by 90 degrees ($\frac{\pi}{2}$ radians).
Worked Example 1: Calculation of Inductive Reactance A choke coil (inductor) used in an old fluorescent light fixture in a Nigerian school has an inductance of 20 H. Calculate its inductive reactance when connected to the national grid with a frequency of 50 Hz.
Solution: Given: Inductance, $L = 20 \, H$ Frequency, $f = 50 \, Hz$ Formula: $X_L = 2 \pi f L$ $X_L = 2 \times 3.142 \times 50 \, Hz \times 20 \, H$ $X_L = 6283 \, \Omega$ (or $6.283 \, k\Omega$)
Answer: The inductive reactance of the choke coil is $6283 \, \Omega$.
Definition: Capacitive reactance ($X_C$) is the opposition offered by a capacitor to the flow of alternating current. It arises from the capacitor's ability to store electric charge.
Explanation: When AC is applied across a capacitor, the capacitor alternately charges and discharges. This charging and discharging process constitutes a current flow. At very low frequencies (or DC), a capacitor charges up and then blocks further current flow. At higher frequencies, it charges and discharges rapidly, effectively allowing more current to pass through. Thus, its opposition to current decreases with increasing frequency.
Formula: $X_C = \frac{1}{2 \pi f C}$ Where: $X_C$ is the capacitive reactance in Ohms ($\Omega$) $\pi$ (pi) is approximately 3.142 $f$ is the frequency of the AC in Hertz (Hz) $C$ is the capacitance of the capacitor in Farads (F)
Key Characteristics: $X_C$ is inversely proportional to frequency ($f$) and capacitance ($C$). At DC ($f=0$), $X_C$ approaches infinity, meaning a capacitor acts as an open circuit (ideally). In a purely capacitive circuit, the current leads the voltage by 90 degrees ($\frac{\pi}{2}$ radians).
Worked Example 2: Calculation of Capacitive Reactance A capacitor used in a power supply filter in a local radio station has a capacitance of 100 microfarads (μF). Calculate its capacitive reactance when operating at a frequency of 10 Hz.
Solution: Given: Capacitance, $C = 100 \, \mu F = 100 \times 10^{-6} \, F$ Frequency, $f = 10 \, Hz$ Formula: $X_C = \frac{1}{2 \pi f C}$ $X_C = \frac{1}{2 \times 3.142 \times 10 \, Hz \times (100 \times 10^{-6} \, F)}$ $X_C = \frac{1}{6.284 \times 10^{-3}}$ $X_C = 159.13 \, \Omega$ Answer: The capacitive reactance of the capacitor is $159.13 \, \Omega$. In AC circuits, inductors and capacitors introduce an opposition to current flow that is different from pure resistance. This opposition is called reactance. Reactance is frequency-dependent and causes a phase shift between voltage and current.
Power Factor Correction in Industries and Homes: Many industries in Nigeria (e.g., manufacturing plants, textile mills) and even some large residential buildings use motors (inductive loads) that cause the current to lag the voltage, leading to a "poor power factor." This wastes energy and incurs penalties from electricity distribution companies (DisCos). Capacitors are often installed in parallel to these inductive loads to introduce leading current, thereby improving the power factor and making the current and voltage more in phase. This reduces energy losses and electricity bills.
Radio and Television Tuning: The ability to tune into specific radio stations (e.g., Wazobia FM, AIT, NTA) on a receiver is a prime example of series resonance. Inside a radio, an RLC circuit (typically an LC tuning circuit) is designed such that its resonant frequency can be adjusted by varying either the capacitance or inductance. When the circuit's resonant frequency matches the frequency of a desired radio station, that station's signal is strongly received or amplified, while other frequencies are largely ignored.
Inverters and Stabilizers: These ubiquitous electronic devices in Nigerian homes and businesses, essential for coping with unreliable power supply, extensively use AC circuit principles. Inverters convert DC from batteries to AC for household appliances, employing circuits that generate and filter specific AC frequencies. Stabilizers use inductive and capacitive components to regulate fluctuating AC input voltages from the grid to provide a stable output, protecting sensitive electronics. The filtering and voltage regulation mechanisms depend on the frequency-dependent behavior of inductors and capacitors.