What must be checked before using the General RL current response relation?

Fix 0⁺, the settled value and τ of the equivalent seen by C or L.

4. First-order transients

General RL current response

Formula

i_L(t)=i_L(\infty)+[i_L(0^+)-i_L(\infty)]e^{-t/\tau}

Detail

The RL current interpolates i0 and i∞ with τ=L/R.

Explore the idea

Variables

$v(t),v_0,v_\infty$ voltages (V)
$i(t),i_0,i_\infty$ currents (A)
$\tau$ time constant (s)
$t$ time (s)
$R,C,L$ Ω, F, H.

Conditions

Piecewise-constant linear first-order circuit; τ>0.

Intuitive explanation

For “General RL current response”: the exponential interpolates the continuous initial value and the settled value with τ.

Worked example

With

i_L(0^+)=1\,\mathrm A

i_L(\infty)=5\,\mathrm A

and

\tau=2\,\mathrm{ms}

i_L(\tau)=3.53\,\mathrm A

Common mistakes

confusing 0⁺ with 0⁻
using τ=L/R on an RC or τ=RC on an RL
forgetting the settled value

Frequently asked questions

What must be checked before using the General RL current response relation?: Fix 0⁺, the settled value and τ of the equivalent seen by C or L.

Also known as

RC transient, RL transient, capacitor charging, exponential discharge

Conventions

V, A or s according to the left-hand side

Last reviewed: 2026-09-19

Found an error? Contact us.

Related formulas

4. First-order transients

General RL current response

In 4. First-order transients

Formula

i_L(t)=i_L(\infty)+[i_L(0^+)-i_L(\infty)]e^{-t/\tau}

Detail

The RL current interpolates i0 and i∞ with τ=L/R.

Explore the idea

Variables

$v(t),v_0,v_\infty$ voltages (V)
$i(t),i_0,i_\infty$ currents (A)
$\tau$ time constant (s)
$t$ time (s)
$R,C,L$ Ω, F, H.

Conditions

Piecewise-constant linear first-order circuit; τ>0.

Intuitive explanation

For “General RL current response”: the exponential interpolates the continuous initial value and the settled value with τ.

Worked example

With

i_L(0^+)=1\,\mathrm A

i_L(\infty)=5\,\mathrm A

and

\tau=2\,\mathrm{ms}

i_L(\tau)=3.53\,\mathrm A

Common mistakes

confusing 0⁺ with 0⁻
using τ=L/R on an RC or τ=RC on an RL
forgetting the settled value

Frequently asked questions

What must be checked before using the General RL current response relation?: Fix 0⁺, the settled value and τ of the equivalent seen by C or L.

Also known as

RC transient, RL transient, capacitor charging, exponential discharge

Conventions

V, A or s according to the left-hand side

Last reviewed: 2026-09-19

Found an error? Contact us.

General RL current response

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas

General RL current response

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Conventions

Related formulas