Lesson Notes By Weeks and Term v4 - SHS 3
ALTERNATING CURRENT
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ALTERNATING CURRENT
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Subject: Physics
Class: SHS 3
Term: 2nd Term
Week: 4
Grade code: 3.3.1.LI.2
Strand code: 3
Sub-strand code: 2
Content standard code: 3.3.1.CS.3
Indicator code: 3.3.1.LI.2
Theme: ELECTRIC FIELD, MAGNETIC FIELD AND ELECTRONICS
Subtheme: ALTERNATING CURRENT
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This lesson introduces the fundamental principles of Alternating Current (AC) circuits, which form the backbone of our national power grid and the electricity we use in our homes every day. Unlike Direct Current (DC) from batteries, AC constantly changes direction. This unique property allows us to use transformers to efficiently transmit power from the Akosombo Dam across Ghana. In this lesson, we will move beyond simple resistance to understand how capacitors and inductors behave in AC circuits.
This section breaks down the core ideas you need to master. We will build from the basics of AC to the rules for analysing circuits. 2.1 From DC to AC: The Basics In your previous studies (and from using batteries), you are familiar with Direct Current (DC). DC flows in one constant direction. Alternating Current (AC), however, periodically reverses its direction. The electricity supplied by the Electricity Company of Ghana (ECG) is AC. It follows a sinusoidal pattern, as shown below. Peak Voltage (V₀) / Peak Current (I₀): The maximum value the voltage or current reaches in either the positive or negative direction. Frequency (f): The number of complete cycles the AC waveform completes in one second. In Ghana, our standard frequency is 50 Hz. 2.2 RMS Values: The "Effective" AC How do we measure an AC voltage that is always changing? We use the Root Mean Square (RMS) value. The RMS value of an AC voltage is the value of a DC voltage that would produce the same amount of heat (power) in the same resistor.
When you see that the voltage from a socket in Ghana is 230 V, this is the RMS voltage (V_rms), not the peak voltage.
The relationship between peak and RMS values is crucial: V_rms = V₀ / √2 (or approximately V_rms = 0.707 * V₀) I_rms = I₀ / √2 (or approximately I_rms = 0.707 * I₀)
Unless a problem specifies "peak voltage," you should always assume the given AC values are RMS. 2.3 Opposition to AC Flow: Resistance, Reactance, and Impedance In DC circuits, the only opposition to current flow is Resistance (R). In AC circuits, capacitors and inductors also oppose current flow, but in a way that depends on the frequency of the AC. Inductive Reactance (X_L): This is the opposition offered by an inductor to the flow of AC. It is caused by the back e.m.f. induced in the coil as the current changes. It increases with frequency. Formula: X_L = 2πfL Where: `f` is frequency (in Hz), `L` is inductance (in Henry, H). `X_L` is measured in Ohms (Ω). Capacitive Reactance (X_C): This is the opposition offered by a capacitor. A capacitor opposes AC by constantly charging and discharging. This opposition decreases as frequency increases. Formula: X_C = 1 / (2πfC) Where: `f` is frequency (in Hz), `C` is capacitance (in Farads, F). `X_C` is measured in Ohms (Ω). Impedance (Z): This is the total opposition to current flow in an AC circuit. It is the combination of resistance and total reactance (X_L - X_C). Formula (for a series circuit): Z = √[R² + (X_L - X_C)²] Impedance `Z` is also measured in Ohms (Ω).