Show that in a pure capacitor joined to an AC source, the current leads the voltage by π/2. Define capacitive reactance and explain why a capacitor blocks DC.

1. 1 · Write the applied voltage. V = V_m cos ωt across a capacitor C.
2. 2 · Find the charge and the current. q = CV_m cos ωt, so I = dq/dt = −ωCV_m sin ωt = ωCV_m cos(ωt + π/2).
3. 3 · Read off the phase. The current reaches its peak a quarter cycle before the voltage: it leads by π/2.
4. 4 · Draw the phasors. [Voltage phasor V drawn horizontal; current phasor I drawn 90° anticlockwise from it; the angle π/2 marked]
5. 5 · Define the reactance. X_C = V_m/I_m = 1/ωC = 1/2πνC, in ohm.
6. 6 · Explain DC. For DC, ν = 0, so X_C is infinite and no steady current flows.
7. 7 · Close in one line. So, a capacitor passes AC more easily at higher frequency, and blocks DC.

Scoring tip: Write the current as a cosine with +π/2 inside the bracket. That line shows the lead clearly.