9702 · 21.1
Characteristics of alternating currents flashcards
Revision flashcards for Cambridge 9702 Characteristics of alternating currents (syllabus 21.1). Flip, recall, then mark a real past-paper question.
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What is an Alternating Current (AC)?
An electric current that periodically reverses its direction and continuously varies its magnitude over time.
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How does AC differ from Direct Current (DC)?
AC reverses direction and varies in magnitude, while DC flows in a constant direction with a steady magnitude.
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What is the 'peak value' of an AC waveform?
The maximum magnitude (amplitude) reached by the voltage or current during a cycle.
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Write the formula for instantaneous AC voltage.
$V = V_0\sin(\omega t)$, where $V_0$ is peak voltage, $\omega$ is angular frequency, and $t$ is time.
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How is angular frequency ($\omega$) related to normal frequency ($f$)?
$\omega = 2\pi f$.
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What is the Root Mean Square (RMS) value of an AC current/voltage?
The DC equivalent value that would dissipate the same average power in a resistor.
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How is RMS voltage related to peak voltage for sinusoidal AC?
$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$
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How is RMS current related to peak current for sinusoidal AC?
$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$
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What is the formula for mean power dissipated in an AC resistor using RMS values?
$\left< P \right> = I_{rms}^2 R = \frac{V_{rms}^2}{R} = V_{rms} I_{rms}$
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How does the mean power relate to the maximum instantaneous power for sinusoidal AC?
The mean power is half the maximum instantaneous power: $\left< P \right> = \frac{1}{2} P_{max}$.
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What is the average value of a sinusoidal AC over one full cycle?
Zero. The positive and negative half-cycles are symmetrical and cancel each other out. This is why the average value is not useful for power calculations.
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Why is the instantaneous power in a resistive AC circuit always positive or zero?
Because power is given by $P = I^2R$. Since the resistance $R$ is positive and the current squared ($I^2$) is always non-negative, the power dissipated is always positive or zero, even when the current itself is negative.
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What is the average value of $\sin^2(\theta)$ over one complete cycle (0 to $2\pi$)?
The average value is 1/2. This mathematical fact is crucial for deducing that the mean power in an AC circuit is half the maximum power, since $\left< P \right> = \frac{1}{2} P_{max}$.