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Technology / Technical guide
DC Capacitor Charging, Initial Voltage & Inrush Current
A capacitor’s voltage state before a connection matters to the ensuing transient. A voltage difference can drive a charging current through the source and interconnection. Inrush concerns that changing state, rather than the steady ripple current or the final stored energy alone.
Initial voltage and the charging path determine the transient.
Capacitance is a storage quantity; source impedance and the voltage history affect the current that changes its state.
01 / Initial condition
A capacitor can begin with stored voltage.
For an ideal constant capacitor, charge and terminal voltage are related by q = Cv.
For an ideal constant capacitor, charge and terminal voltage are related by q = Cv. The initial voltage is therefore part of its electrical state. A capacitor described as uncharged is a particular initial condition, not an automatic property of every shutdown or restarted circuit.
The difference between source voltage and initial capacitor voltage influences the ensuing charge transfer. Two otherwise identical circuits can have different transients if they begin in different states. A final voltage reading alone does not disclose the earlier current history.
02 / Charging current
Voltage slope connects storage to current.
Under a consistent capacitor reference, i = C dv/dt.
Under a consistent capacitor reference, i = C dv/dt. A given voltage change completed over a shorter time involves a larger average charging current for the same constant C. TI’s inrush explanation uses this capacitance-to-voltage-slope relationship for a changing supply boundary.
That relation does not independently choose the slope in a complete circuit. Source behaviour, interconnection impedance, other branches and limits influence it. An ideal zero-impedance voltage step is a mathematical extreme, not a real-world assumption that can define an acceptable equipment current.
03 / Restricted RC model
A resistor and fixed source give an exponential result.
Consider only a constant source Vs connected through a constant positive resistance R to a constant capacitor C, with initial voltage V0 and no other load.
Consider only a constant source Vs connected through a constant positive resistance R to a constant capacitor C, with initial voltage V0 and no other load. For t ≥ 0, vC = Vs + (V0 − Vs)e^(−t/RC), and current toward the capacitor is i = (Vs − V0)e^(−t/RC)/R.
These equations state a hypothetical linear circuit. If Vs is above V0, current initially charges the capacitor; changing the relative voltages changes the sign in that bidirectional ideal model. It does not prove that an actual power supply accepts reverse current or that a converter contains this arrangement.
04 / Time scale
One time constant closes a fraction of the initial gap.
The RC time constant is τ = RC in seconds.
The RC time constant is τ = RC in seconds. At t = τ, the remaining voltage difference from the final value is e^(−1), about 36.8% of its initial magnitude. About 63.2% of that original gap has closed in this model.
The result describes a fraction of a gap, not necessarily 63.2% of final voltage when V0 is nonzero. Exact equality with Vs is approached asymptotically in the ideal model. No actual resistance, capacitance, waiting time or startup permission is supplied.
05 / Energy and loss
Final stored energy is not the entire source transfer.
The ideal capacitor’s stored-energy change is ½C(Vs² − V0²) for the specified endpoints.
The ideal capacitor’s stored-energy change is ½C(Vs² − V0²) for the specified endpoints. In the restricted resistive charging model, energy also dissipates in the resistor during transfer. A capacitor’s final energy does not mean every joule supplied became useful stored energy.
This transient loss differs from repeated ripple heating during operation. The ripple-current guide concerns a different waveform boundary, while the energy-accounting guide includes changes in storage explicitly.
06 / Model scope
Inrush explanation does not disclose startup hardware.
A real source may ramp, limit or interact with more than one storage element.
A real source may ramp, limit or interact with more than one storage element. Such behaviour requires another model instead of retaining the restricted RC solution without its assumptions. A circuit name also cannot establish an implemented precharge function or completed charging state.
No MARSTON inrush value, startup circuit, initial discharge state or capacitor parameter is assigned. The explanation provides no energisation sequence, resistor sizing, contactor timing or discharge procedure; it describes the dependence of a transient on an initial state and defined path.
Related technical guides: Converter Instantaneous Power, Storage & Dissipation · Thermal Resistance, Heat Capacity & Transient RC Models · Parasitic Inductance, Current Slew & Switching Overshoot.
General background: Texas Instruments: capacitor charging current and inrush boundaries. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Initial state | V0 and q0 = CV0 | Uncharged is a specified initial condition. |
| Charging relation | i = C dv/dt | Constant capacitor and declared current direction. |
| RC solution | Exponential approach to fixed Vs | Positive constant R/C, no other branch or load. |
| Time constant | τ = RC in s | Gap decays to e^(−1) after one τ. |
| Energy balance | Stored-energy change and dissipation | Final storage is not all source energy. |
Engineering questions.
Is every capacitor initially at zero voltage?
No. Initial voltage is part of the circuit state.
Does capacitance alone determine the current peak?
No. The source, path and voltage history also matter.
Does one τ mean 63.2% of final voltage in every case?
No. It closes that fraction of the original voltage gap in the stated RC model.
Does the ideal reverse-current solution prove supply capability?
No. A physical source may not support that direction.
Are inrush and steady ripple the same mechanism?
No. They describe different current histories and storage conditions.
Does this specify a MARSTON precharge or startup sequence?
No actual circuit, parameter or operational procedure is assigned.
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