A voltmeter is often treated as an invisible observer. Put it across a slowly discharging capacitor and its input resistance becomes another route for charge to leave. In this experiment the instrument can halve the nominal decay time. That is a useful result, provided we calculate the circuit we actually connected.
Verification: this design and calculator have not been physically tested. The curves are calculated ideal examples. The supplied observation sheet is blank. Host software checks do not establish the input resistance, leakage or capacitance of your hardware.
Use a regulated 3.3 V direct-current (DC) supply, a single-pole single-throw (SPST) switch, a breadboard, a digital voltmeter, one 1 kΩ resistor and two 10 MΩ ±1% resistors rated at least 0.25 W. A megohm, written MΩ, is one million ohms. The first 10 MΩ part is the permanent discharge resistor R2; the second is optional R3 for a comparison run.
C1 is a WIMA MKS 2 metallized polyester film capacitor, 1.0 µF, 63 V DC, ±10%, 5 mm lead spacing. The current March 2026 manufacturer table gives base MKS2C041001F00; completing it with K tolerance, S bulk packing and SD lead length gives MKS2C041001F00KSSD. Its listed body is 5 × 10 × 7.2 mm. Check the delivered marking and order specification. An older 50 V MKS 2 ordering code is not the same current table entry. This nonpolar film part avoids the polarity issue of an electrolytic capacitor; its insulation still is not infinite.
The 63 V marking is a component rating, not this experiment's operating voltage. Work only at 3.3 V on this isolated bench circuit. R1 limits initial charging current to about 3.3 mA. R2 makes the decay repeatable enough to compare instruments. The meter contributes its own parallel input resistance RM. You must obtain that value for the selected voltage range from your actual meter manual; do not assume that every meter, range or oscilloscope probe is 10 MΩ.
A breadboard has conductive strips hidden under its surface. Check which holes join before inserting the 5 mm capacitor leads; placing both leads in one strip shorts the capacitor. Clean, dry wiring matters because surface leakage becomes visible at megohm resistance. Long jumper wires and nearby hands can also add capacitance or pickup. Do not use this as a measurement method for a powered device or a charged unknown capacitor.
A time constant τ describes exponential decay: after one τ the remaining voltage is about 36.8% of its initial value. For an ideal capacitor C discharging through a resistance R, τ = RC. With R2 and RM in parallel, their conductances add: Req = 1 / (1/R2 + 1/RM). Conductance is the ease of current flow, the reciprocal of resistance.
For R2 = RM = 10 MΩ, Req = 5 MΩ. With C = 1 µF, τ = 5 s. Ignoring the meter gives 10 s, twice the value of the circuit actually connected. Adding R3 = 10 MΩ gives three equal parallel paths: Req = 3.333 MΩ and τ = 3.333 s. These are nominal calculations; resistor tolerance, capacitor tolerance and other leakage still apply.
During charge, R1 and Req form a divider. With Req = 5 MΩ, the ideal steady VC is 3.3 × 5,000,000 / 5,001,000 ≈ 3.29934 V. The charge time constant is approximately (1 kΩ || 5 MΩ) × 1 µF ≈ 1 ms. A manual meter is much slower than that transient. Read the actual charged voltage; do not force the fit to an assumed 3.30000 V.
The orange curve shows a hypothetical circuit without an attached meter. You cannot obtain that curve merely by connecting the same meter and labelling it unloaded. A different measurement method also has loading that must be considered. All three curves are normalized to their own starting voltage V0, so their comparison emphasizes decay rate rather than small charging-divider differences.
No firmware is necessary. Save the complete Python 3 program below as rc_discharge.py on your computer. It accepts two positive falling voltage readings and their elapsed time, calculates τ, then estimates capacitance using the resistance paths you supply. Units are seconds, volts and ohms. Its example is synthetic arithmetic, not a measurement log.
"""Conditional RC discharge calculator; no measurement interface or invented data."""
import math
def positive_finite(value, name):
value = float(value)
if not math.isfinite(value) or value <= 0:
raise ValueError(name + ' must be finite and positive')
return value
def parallel_ohms(*paths):
if not paths:
raise ValueError('provide at least one real resistance path')
values = [positive_finite(x, 'resistance') for x in paths]
reciprocal = sum(1.0 / x for x in values)
if not math.isfinite(reciprocal) or reciprocal <= 0:
raise ValueError('resistance scale is not representable')
result = 1.0 / reciprocal
return positive_finite(result, 'equivalent resistance')
def tau_from_points(t1, v1, t2, v2):
t1, t2 = float(t1), float(t2)
if not math.isfinite(t1) or not math.isfinite(t2) or t2 <= t1:
raise ValueError('finite time must advance')
v1 = positive_finite(v1, 'v1')
v2 = positive_finite(v2, 'v2')
if v2 >= v1:
raise ValueError('voltage must fall strictly above zero')
# Difference of logarithms avoids underflow of v2/v1.
ratio_increment = (v1 - v2) / v2
denominator = (math.log1p(ratio_increment) if math.isfinite(ratio_increment)
else math.log(v1) - math.log(v2))
result = (t2 - t1) / denominator
return positive_finite(result, 'time constant')
def capacitance_from_points(t1, v1, t2, v2, *resistance_paths):
tau = tau_from_points(t1, v1, t2, v2)
return positive_finite(tau / parallel_ohms(*resistance_paths), 'capacitance')
if __name__ == '__main__':
tau = tau_from_points(0, 2.0, 5, 2.0 / math.e)
cap = capacitance_from_points(0, 2.0, 5, 2.0 / math.e, 10e6, 10e6)
print('Synthetic example only: tau={:.6g} s; C={:.6g} F'.format(tau, cap))
Run python3 rc_discharge.py to reproduce the nominal example: 2.0 V falling to 2/e V in 5 seconds gives τ = 5 s and C = 1 µF with two 10 MΩ paths. To use your observations, replace the example's readings, times and resistor values explicitly. Add R3 as a third argument to parallel_ohms. Keep the original blank sheet and create a separate dated result file.
The calculator refuses zero, negative, equal or rising voltages; reversed or identical times; nonfinite numbers; and nonpositive resistances. It cannot tell whether plausible numbers came from a real discharge. A disconnected lead, stale display or range change can produce misleading but positive values. Validation of numbers is necessary and insufficient for validation of an experiment.
Dielectric absorption is a slow redistribution of stored charge inside the insulating material; after a capacitor is discharged and left open, a small voltage may reappear. A simple one-exponential model omits that behavior. The manufacturer also specifies insulation under particular test conditions, not a promise that a dirty breadboard at 3.3 V has exactly that resistance. Meter timing uncertainty is especially important if only a few display updates span the decay.
Two voltage points identify a time constant under the assumed model. They do not separately identify C and every unknown leakage resistance. If RM is unknown, calculating C as τ/R2 silently assigns meter and surface leakage to the capacitor. Report the measured decay and the assumptions before giving a capacitance estimate. An apparent disagreement with the ±10% capacitor marking can be an instrument problem or a model problem.
With R2 = 10 MΩ, Req = 10/11 MΩ ≈ 0.909 MΩ, so the nominal τ for 1 µF becomes about 0.909 s. Using the false 10 MΩ meter assumption would estimate only about 0.182 µF. The capacitor did not lose four fifths of its value; the calculation used the wrong observer.
For related reading, start with measuring LED current through a resistor: both experiments infer one quantity from a voltage measurement and a model. The two methods have different loading and timing limits.
The component family, dimensions, ratings and ordering completion were checked in the WIMA MKS 2 datasheet, March 2026, also listed in the manufacturer's 2026 catalogue. There is no microcontroller or target executable in this build. Host tests exercise the delivered calculator and refusal paths; the circuit, instrument timing and real component values await owner bench measurements.