All Labs

RC/RL Transients Lab

Select a circuit type, adjust resistance, capacitance or inductance, and supply voltage, then watch voltage and current evolve on an oscilloscope-style display. Measure time constants, verify the exponential model, and use semilog analysis to extract experimental values of τ.

Guided Experiment: Measuring RC Time Constant

When a capacitor charges through a resistor, what fraction of the supply voltage will it reach after one time constant τ = RC? How many time constants until the capacitor is essentially fully charged?

Write your hypothesis in the Lab Report panel, then click Next.

Circuit Diagram

S+−5.0VR = 1.00 kΩC = 100 µF
Type
RC Charging
τ
100.00 ms
5τ (99% complete)
500.00 ms

Oscilloscope

Controls

Resistance (R)1.00 kΩ
Capacitance (C)100 µF
Supply Voltage (V₀)5.0 V

Results

VC(t)=V0(1−e−t/τ)=5.0(1−e−t/0.1000)V_C(t) = V_0\left(1 - e^{-t/\tau}\right) = 5.0\left(1 - e^{-t/0.1000}\right)
Time Constant
τ = 100.00 ms
τ=RC=1.00kΩ×100µF\tau = RC = 1.00 k\Omega \times 100 µF
Voltage
0.000 V
Current
5.000 mA
Energy
0 J
% Complete
0.0%
Elapsed Time
0 s
t / τ
0.00
RC Charging — R = 1.00 kΩ, C = 100 µF, V₀ = 5.0 V

Data Table

(0 rows)
#TrialCircuitt(s)V(V)I(mA)τ(s)% Completeln(V/V₀)
0 / 500
0 / 500
0 / 500

Reference Guide

RC Circuit Transients

When a capacitor charges through a resistor, the voltage rises exponentially toward the supply voltage with time constant τ = RC.

VC(t)=V0(1−e−t/τ)V_C(t) = V_0\left(1 - e^{-t/\tau}\right)

During discharge, the voltage decays exponentially from its initial value toward zero.

VC(t)=V0⋅e−t/τV_C(t) = V_0 \cdot e^{-t/\tau}

At t = τ the charging capacitor reaches 63.2% of the supply voltage. At t = 5τ it is essentially fully charged (99.3%).

RL Circuit Transients

When current builds through an inductor, it rises exponentially toward V₀/R with time constant τ = L/R.

I(t)=V0R(1−e−t/τ)I(t) = \frac{V_0}{R}\left(1 - e^{-t/\tau}\right)

During de-energizing, the current decays exponentially while the inductor generates a back-EMF to oppose the change.

I(t)=V0R⋅e−t/τI(t) = \frac{V_0}{R} \cdot e^{-t/\tau}

The inductor voltage V_L starts at the full supply voltage and drops to zero as the current reaches steady state.

Semilog Analysis

For an RC discharge, taking the natural log of both sides gives a linear relationship between ln(V/V₀) and time.

ln⁡(VCV0)=−tτ\ln\left(\frac{V_C}{V_0}\right) = -\frac{t}{\tau}

Plotting ln(V/V₀) vs t produces a straight line with slope −1/τ. This technique is useful for extracting time constants from noisy experimental data because the linear fit is more robust than fitting an exponential directly.

The same approach works for RL de-energizing using ln(I/I₀) = −t/τ.

Energy Storage

Capacitors store energy in the electric field between their plates. The energy depends on the square of the voltage.

EC=12CV2E_C = \frac{1}{2}CV^2

Inductors store energy in their magnetic field. The energy depends on the square of the current.

EL=12LI2E_L = \frac{1}{2}LI^2

During charging, exactly half the energy from the source is stored in the capacitor; the other half is dissipated as heat in the resistor. This is true regardless of the value of R.