Characteristics of alternating currents
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Define the terms period (T) and frequency (f) as they relate to alternating current (AC).
Period (T) is the time taken for one complete cycle of the AC waveform, measured in seconds. Frequency (f) is the number of complete cycles per second, measured in Hertz (Hz). They are inversely related: f = 1/T.
An alternating voltage is represented by V = V₀ sin(ωt). What do V₀ and ω represent?
V₀ represents the peak voltage, which is the maximum voltage reached during a cycle. ω represents the angular frequency, where ω = 2πf, and f is the frequency in Hertz.
For a sinusoidal alternating current, what is the relationship between the peak current (I₀) and the root-mean-square (r.m.s.) current (Iᵣₘₛ)?
The r.m.s. current (Iᵣₘₛ) is related to the peak current (I₀) by the equation: Iᵣₘₛ = I₀ / √2. The r.m.s. value is the effective value of the AC, equivalent to the DC value that would produce the same heating effect.
A 230V AC supply is quoted. Is this the peak voltage or r.m.s voltage?
This is the r.m.s. voltage. Domestic AC supplies are always quoted as the r.m.s. voltage.
How is the mean power (P_mean) dissipated in a resistive load related to the maximum power (P_max) for a sinusoidal alternating current?
The mean power (P_mean) is half the maximum power (P_max): P_mean = ½ P_max. This is because the power varies sinusoidally over time, and the average power is half the peak power.
Describe how you would use an oscilloscope to determine the period and peak voltage of an alternating voltage signal.
On the oscilloscope, the period (T) can be determined by measuring the time for one complete cycle on the time axis (x-axis), and then using the timebase setting. The peak voltage (V₀) can be determined by measuring the maximum vertical deflection on the voltage axis (y-axis) and then using the volts/division setting.
State the equation that relates the r.m.s. voltage (Vᵣₘₛ) to the peak voltage (V₀) for a sinusoidal alternating voltage.
Vᵣₘₛ = V₀ / √2.
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