If the voltage across a capacitor is V = V max sin(2ft), the charge on the capacitor is also proportional to sin(2ft) (see Eq. 22.17).

If the voltage across a capacitor is V = V_max sin(2πft), the charge on the capacitor is also proportional to sin(2πft) (see Eq. 22.17). The current through the capacitor in this case is given by I = I_max sin(2πft + π/2); hence, the phase angle is  ϕ = π/2 radians relative to the voltage. Suppose we begin instead by assuming the capacitor voltage is proportional to a cosine function V = V_max cos(2πft). Use a graphical argument to show that the current is now given by a function of the form I = I_max cos(2πft + π/2) so that the phase of the current relative to the voltage is again ϕ = π/2 rad.