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A-LEVEL 9702 · A2 · TOPIC 21
Alternating currents
The chain of the topic: a sinusoid x = x₀ sin ωt fixes the peak, period and frequency, the r.m.s. value gives the steady d.c. that delivers the same mean power, then a diode rectifies the a.c. and a capacitor smooths it into usable d.c. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 21: ALTERNATING CURRENTS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T17 Oscillations: sin ωt T19 Capacitance: RC T20 Magnetic fields: induction 21.1
21.1
21.2
21.2
TOPIC 21
ALTERNATING
CURRENTS
1 · THE SINUSOIDAL A.C.
Current that reverses, traced as a sine wave.
Sinusoidal a.c.: x = x₀ sin ωt (x is I or V)
x₀ is the peak value; it swings from +x₀ to −x₀
Period T, frequency f, angular frequency ω
ω = 2πf = 2π / T
mains: f = 50 Hz
t
x
x₀
T
2 · R.M.S. VALUES & MEAN POWER
The steady d.c. that delivers the same power.
Power ∝ I², so the mean of I² is what matters.
For a sinusoid the mean power is half the peak.
R.m.s. value = peak ÷ √2 for a sine wave only.
I_rms = I₀/√2 V_rms = V₀/√2
<P> = ½P₀ = I_rms² R = V_rms²/R
t
P
<P> = ½P₀
P₀
3 · RECTIFICATION
Diodes force the current one way only.
A diode conducts in one direction: it blocks reverse.
Half-wave: one diode removes the negative halves.
Full-wave: a four-diode bridge flips them upward.
Output is bumpy but always one sign: not steady yet.
input a.c.
full-wave output
4 · SMOOTHING
A capacitor flattens the ripple to near d.c.
A capacitor in parallel with the load stores charge.
It charges at the peak, then discharges through R.
Larger C or larger R: bigger RC, less ripple.
Result: a steadier d.c. that can power electronics.
time constant τ = RC
t
V
smoothed
small ripple remains
LEADS TO
T20 Magnetic fields: transformers carry a.c. power T22 Quantum physics: the diode as a junction T24 Medical physics: smoothed d.c. drives detectors The thread: r.m.s. quantifies the power an a.c. delivers, and rectifying plus smoothing turns the supply into the steady d.c. that real instruments need.
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