Alternating Current Equations

Overview

This lesson introduces the core language and equations for alternating currents. You will connect period, frequency, angular frequency, peak value, mean power, and r.m.s. values to sinusoidal current and voltage graphs.

What You Need to Know

• Alternating current and voltage change direction and magnitude periodically.
• Period is the time for one complete cycle; frequency is the number of cycles per second.
• Peak value is the maximum value of the alternating current or voltage.
• Sinusoidal a.c. can be modelled with equations of the form x = x0 sin omega t.
• For a sinusoidal a.c. in a resistive load, mean power is half the maximum power.
• R.m.s. values allow an a.c. current or voltage to be compared with an equivalent d.c. value.

How to Work Through It

1. Start by reading a sinusoidal graph and identifying amplitude, period, and peak value.
2. Convert between period, frequency, and angular frequency where needed.
3. Use sinusoidal equations to find current or voltage at a given time.
4. Practise peak, r.m.s., maximum power, and mean power calculations.

Check Your Understanding

• How do you find frequency from the period of an a.c. waveform?
• What is the difference between peak and r.m.s. values?
• Why is mean power in a resistive load half the maximum power for a sinusoidal a.c.?
• What information do you need before using x = x0 sin omega t?

Common Mistakes

• Treating peak and r.m.s. values as interchangeable.
• Using degrees instead of radians when working with omega t.
• Forgetting that the sign of current or voltage changes during the cycle.
• Using maximum power when the question asks for mean power.

Next Steps

• Keep graph reading and r.m.s. conversions secure before rectification.
• Bring the waveform shapes into the next lesson on diode circuits.