5.000 V DC step source
Provide a constant applied voltage E from t = 0.
Physics / RC charging time constant
FREE TO EXPLOREEXPERIMENT 09 · PHYSICS LABORATORY
RC charging and the capacitor time constant
Determine the charging time constant of an RC circuit from capacitor-voltage observations and a logarithmic graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
CAPACITOR VOLTAGE VC—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
The model uses E = 5.000 V, R = 10,000 Ω and C = 100 μF, with zero initial voltage, instantaneous source switching, exact elapsed times and no leakage, equivalent series resistance, dielectric absorption or meter loading. Vc is rounded to 0.001 V. Each requested observation starts an identical transient. The unweighted logarithmic fit treats times as exact and does not model the voltage-dependent uncertainty introduced by transformation. The generator calculates Vc = 5[1 − exp(−t/1.000)] V and rounds to 0.001 V. Analysis uses x = t and y = ln[5/(5 − Vc)], estimating τ = 1/gradient. The reference 1.000 s is the product of the fixed model R and C, not a measurement of actual components.
Know your apparatus.
10.0 kΩ resistor
Limit charging current and set the resistance in the model time constant.
100 μF capacitor
Store charge; preserve polarity and voltage rating when using a physical polarized capacitor.
Switch and voltage-time recorder
Start charging from an initially discharged state and sample capacitor voltage with adequate time resolution.
FOLLOW THE METHOD
A reason behind every step.
Determine the charging time constant of an RC circuit from capacitor-voltage observations and a logarithmic graph. Suggested independent settings: 0.2, 0.6, 1, 1.8, 2.6 s.
Prepare the discharged state
With a physical source disconnected, discharge through a suitable resistor and verify near-zero capacitor voltage. Check component polarity and ratings before wiring.
Why this step matters
The model solution requires Vc(0) = 0 and safe physical handling requires controlled discharge.
Set the source and timing reference
Use E = 5.000 V and identify t = 0 as the start of the applied voltage step. Choose a recording method suited to a roughly one-second transient.
Why this step matters
A time-origin error changes the transformed intercept.
Read the charging voltage
Choose an elapsed time in the 0.2–3.0 s range and request the capacitor-voltage observation. Record Vc in volts and time in seconds.
Why this step matters
The measured quantity is capacitor voltage, not resistor voltage.
Gather distinct times
Collect at least five distinct times across the range. Each model observation restarts the same initially discharged transient; real repeat runs require a verified discharge first.
Why this step matters
A common initial condition makes measurements comparable.
Transform and plot
Check that Vc is below E. Calculate E − Vc, then the dimensionless ratio E/(E − Vc), then its natural logarithm. Fit this logarithm against time.
Why this step matters
The positive logarithm yields a positive slope equal to 1/τ.
Calculate and assess
Use τ = 1/m in seconds. Compare with RC = 1.000 s, inspect the intercept and residuals, and discuss voltage-dependent transformed uncertainty and timing calibration.
Why this step matters
Agreement with model components is a consistency check rather than independent proof of their accuracy.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
Vc = E(1 − exp(−t/τ)); ln[E/(E − Vc)] = mt + b; τ = 1/m
| # | Elapsed charging time t (s) | Capacitor voltage Vc (V) | Elapsed time t (s) | ln[E/(E − Vc)] | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING