Capacitive Voltage Dividers
2 min read
Quick Answer
Two capacitors in series divide an alternating voltage between them. Because the same charge sits on both, the voltage splits in inverse proportion to capacitance, and the ratio comes out the same at every frequency. The divider dissipates almost nothing, which is its advantage over a resistive one.
Read it either way and the answer agrees. In charge terms, a series pair carries one charge, so each part shows that charge divided by its own capacitance and the smaller capacitance takes the larger share. That is the argument capacitors in series and parallel sets out. In reactance terms it is an ordinary voltage divider with reactances in place of resistances, and since both reactances carry the same factor of frequency, the frequency cancels and the ratio is flat.
Two conditions keep it honest. It divides changing voltages only: at steady DC the capacitances pass nothing, and where the tap sits is then decided by the parts' leakage resistances rather than by either capacitance. And the tap has to feed a high impedance, because a resistive load turns the pair into a high-pass network whose ratio does depend on frequency after all. That is the mechanism inside a scope probe, where the trimmer sets the capacitive division to match the resistive one so that ten to one holds at DC and at speed alike.
Safety
The same arrangement drops mains voltage in transformerless supplies, and there it is lethal by construction. Nothing isolates the low-voltage side, so every point in the circuit can sit at mains potential even where a meter reads a few volts, and the capacitor holds charge after the supply is disconnected. Do not probe, service or breadboard one. Where isolation is wanted, the part that provides it is a transformer, not a capacitor.