In a capacitor, which statement best describes the phase relationship between current and voltage?

In a capacitor, which statement best describes the phase relationship between current and voltage?

• A. Voltage leads current
• B. They are in phase
• C. Current leads voltage
• D. Current lags voltage

Answer: (C)

In a capacitor, current is tied to how fast the voltage across the capacitor changes. Mathematically, i = C dv/dt. If the voltage is a sinusoid v(t) = Vp sin(ωt), then i(t) = Vp ωC cos(ωt), which can be written as i(t) = Vp ωC sin(ωt + 90°). That means the current waveform sits a quarter cycle ahead of the voltage waveform—the current leads the voltage by 90 degrees. Intuitively, as the voltage starts to rise, current flows to charge the capacitor; the steepest slope (maximum current) occurs when the voltage crosses zero, while when voltage is at a peak (slope zero) the current is zero. This contrasts with an inductor, where current lags voltage, and a resistor, where current and voltage are in phase.

In a capacitor, current is tied to how fast the voltage across the capacitor changes. Mathematically, i = C dv/dt. If the voltage is a sinusoid v(t) = Vp sin(ωt), then i(t) = Vp ωC cos(ωt), which can be written as i(t) = Vp ωC sin(ωt + 90°). That means the current waveform sits a quarter cycle ahead of the voltage waveform—the current leads the voltage by 90 degrees. Intuitively, as the voltage starts to rise, current flows to charge the capacitor; the steepest slope (maximum current) occurs when the voltage crosses zero, while when voltage is at a peak (slope zero) the current is zero. This contrasts with an inductor, where current lags voltage, and a resistor, where current and voltage are in phase.