RC charging voltage at time calculator

When a DC step is applied through a resistor onto an initially uncharged capacitor, the plate voltage does not jump; it climbs along the classic exponential RC charge curve toward the supply. Engineers, students, and firmware authors often need the voltage at one specific time rather than a full plot: V_c of t equals V_s times one minus e to the minus t over R C, with R in ohms, C in farads, V_s in volts, and t in seconds. This RC charging voltage at time calculator accepts those four finite numbers, returns the capacitor voltage, the time constant τ equals R C, the charge fraction, stored charge, and the series current when it is finite, and rejects negative elapsed time with a clear validation error.

How voltage rises on a series RC charge curve

Start from Kirchhoff's voltage law on a loop that contains a constant supply V_s, a series resistor R, and a capacitor C that begins uncharged. The resistor current equals C times dV_c over dt, so the capacitor voltage obeys the first-order linear ODE R C dV_c over dt plus V_c equals V_s.

With V_c of zero equal to zero at the switching instant, the unique closed-form solution is V_c of t equals V_s times one minus the exponential of minus t over tau, where the time constant tau equals R times C. At t equals zero the voltage is zero; after one tau it has reached about sixty-three point two percent of the supply; after three tau roughly ninety-five percent; and after five tau about ninety-nine point three percent, the classic settling rule of thumb.

The complementary current is I of t equals V_s over R times e to the minus t over tau: large at the first instant and decaying toward zero as the capacitor approaches open circuit at DC. Stored charge on the plates is simply C times the instantaneous voltage, so once V_c is known the coulomb count follows without a second differential equation.

The model assumes ideal linear parts, no dielectric absorption, and a pure step applied at t equals zero; real switches, ESR, and leakage add second-order effects that belong on separate analysis paths. Energy stored is one half C V_c squared and is not the primary output here, because search intent for charging voltage at a chosen time differs from search intent for energy or for the bare product Q equals C V at a fixed bias.

Where RC charging voltage at time shows up in real work

Introductory electronics labs constantly assign RC charging plots so students can mark one-tau and five-tau milestones on a scope before they move on to discharge and multi-stage filters. Embedded and power-electronics bring-up teams estimate how long a soft-start RC or a reset supervisor network needs before a rail has reached a fraction of the final supply, then convert that delay into firmware timeouts and brown-out margins.

Analog designers sizing sample-and-hold windows, peak detectors, and RC timing blobs need V_c of t rather than only the bare time constant, because percent-of-final voltage is the acceptance criterion on the bench. Keep the static Q equals C V product, the tau equals R C time-constant-only landing, energy one half C V squared, and discharge-from-initial-voltage calculators on separate pages so each search intent has one clear tool rather than an overloaded multi-formula page that confuses both students and search engines.

When you only need the voltage at one timestamp on the charge curve, this RC charging voltage at time calculator is the direct contract: four numbers in, V_c and the supporting tau and fraction fields out, with no symbolic solver and no network hop.