Sinusoidal a.c. Equations
Sinusoidal a.c. Equations
- A sinusoidal current moves through the same smooth cycle again and again. Read that cycle before reading its equation.
Read the wave before the symbols
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- The vertical distance from zero to a peak gives the peak current.
- The horizontal distance between matching points gives one period.
- A sine wave with no phase shift starts at zero and moves upward. A cosine wave with no phase shift starts at a positive peak.
Peak current controls the height of the wave. Frequency controls how quickly the cycles repeat.
Read the peak and angular frequency
The equation stores the same two features: the number before sine is the peak, and the number multiplying time controls how quickly the wave repeats.
Symbols
- = instantaneous current (A)
- = peak current (A)
- = angular frequency (rad s⁻¹)
- = time (s)
- The number before sine is the peak value.
- The number multiplying time is angular frequency, not frequency. Divide it by to find the frequency.
- A sine graph with no phase shift starts at zero and first moves upward. A cosine graph with no phase shift starts at a positive peak.
Equation to timing, one decision at a time
Worked example
Read before calculating
Find the peak current, frequency and period for:
- The peak current is the coefficient before sine.
- The angular frequency is rad s⁻¹.
- Use the frequency to find the period.
Answer
The same values and a two-cycle sketch were assessed in 2024 (9702/42/O/N/24 Q8(b)).
Common mistake
If the equation contains , the π is already part of the angular frequency. Do not multiply by another π.
Your turnequation check
A voltage is given by V = 12 sin(100πt), with V in volts and t in seconds. State its peak voltage, frequency and period.
Show worked answer
Answer