Capacitors of Various Capacitances

Compare the currents through three capacitors at the same voltage and frequency. Larger capacitance draws proportionally more AC current. Each source has a 1 V peak sinusoidal output. All branches share one ideal voltage source at 100 Hz.

Capacitors respond to the rate of change of voltage: current is greatest when voltage crosses zero.

Calculate the response

$$\begin{aligned} i_C&=C\frac{dv}{dt}\\ |X_C|&=\frac{1}{2\pi fC}\\ I_{\mathrm{pk}}&=2\pi fC V_{\mathrm{pk}} \end{aligned}$$

Branch	Value	Frequency	Peak current
C1	1 µF	100 Hz	0.62832 mA
C2	2 µF	100 Hz	1.2566 mA
C3	4 µF	100 Hz	2.5133 mA

$$\begin{aligned} v(t)&=V_{\mathrm{pk}}\cos(2\pi f t)\\ i(t)&=-I_{\mathrm{pk}}\sin(2\pi f t) \end{aligned}$$

Current leads voltage by 90°, or one quarter-cycle. At 100 Hz, one cycle is 10 ms and one quarter-cycle is 2.5 ms. All tabulated amplitudes are peak, not RMS; divide by $\sqrt{2}$ for RMS.

Read the schematic and chart

The green V probe reads the shared voltage. I1 is blue, I2 purple and I3 orange; each arrow points down into its branch. A negative current means flow opposite the probe arrow.

The chart stacks voltage above current so volts and amperes have separate scales. The saved view shows 10–40 ms; the simulation runs from 0 to 40 ms with a 10 µs maximum step. Open Table for matching time samples and named columns. Compare current amplitudes at the same instant.

Each source uses Phase = 90°, so its sine waveform begins at a cosine peak. Use initial conditions is enabled. Capacitors start at 1 V and inductors at 0 A; those values match the chosen steady sinusoid and avoid an artificial charging impulse or DC current offset. Initial samples are outside the saved chart view.

Try two changes

1. Double V1 → Frequency from 100 to 200 Hz and run again. Each peak current doubles, and each waveform completes twice as many cycles. Restore the original frequencies.
2. Double every capacitor’s Capacitance and run again. Peak current doubles at the same frequency. The relative current ratios stay the same. Restore the displayed values afterward.

Model assumptions

These are ideal linear components and ideal sources. The reactive component exchanges energy with the source and consumes zero average real power in this ideal model. Real parts add leakage, winding resistance, ESR and parasitic reactance; inductors can saturate. The chosen initial energy is intentional and does not model connecting an unenergized part to a live source.