Characteristics of an alternating current
Section: Alternating Currents | Syllabus: Cambridge AS Level Physics 9702
Characteristics of an alternating current Alternating e.m.f. and potential difference Definitions: Alternating Current (a.c.): A current that periodically varies from positive to negative and changes its direction.
Alternating Voltage: A potential difference that changes polarity with time. Waveform Terminology: Peak Value (x_0): The maximum magnitude of the quantity (current or voltage) from zero. Peak-to-Peak Value: The difference between the maximum positive and maximum negative values (2x_0).
Period (T): The time taken for one complete cycle of oscillations. Unit: second (s). Frequency (f): The number of complete cycles per unit time. Unit: Hertz (Hz). Relationship between Period and Frequency: T = 1/f Angular Frequency (ω): ω = 2π f = 2π/T Unit of ω: radians per second (rad \ s^-1).
Sinusoidal Nature An alternating current is often produced by a coil rotating at a constant speed in a uniform magnetic field. This uniform circular motion results in a sinusoidal waveform. One complete rotation (2π radians) corresponds to one complete cycle of the alternating quantity.
Instantaneous values at time t: ε = ε_0 ω t V = V_0 ω t I = I_0 ω t Important Since ω is in rad \ s^-1, your calculator MUST be in RADIANS mode when performing calculations involving ω t. Worked Examples Worked Example Question: The mains supply in a country has a peak voltage of 311 V and a frequency of 50 Hz.
Write an equation for the potential difference V in terms of time t. Solution: Identify constants: V_0 = 311 V, f = 50 Hz. Calculate angular frequency: ω = 2π f = 2π(50) = 100π 314 rad s^-1. Substitute into general equation: V = V_0 ω t.
Answer: V = 311 (100π t) Common Exam Error Do not confuse frequency (f, in Hz) with angular frequency (ω, in rad s⁻¹). The equation is (2π f t), simply writing (ft) is incorrect.
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