What must be checked before using the Sinusoidal signal relation?

Work in RMS, convert f to ω=2πf and keep reactance signs.

6. AC and phasors

Sinusoidal signal

Formula

v(t)=V_p\cos(\omega t+\phi)

Detail

The sinusoid v(t)=Vp cos(ωt+φ) is the projection of the rotating phasor.

Explore the idea

Variables

$V_p$ peak (V)
$V_{\mathrm{rms}}$ RMS (V)
$\omega$ rad/s
$f$ Hz
$\phi$ rad
$Z,X$ Ω
$Y$ S.

Conditions

Sinusoidal steady state; RMS phasors unless a peak is stated.

Intuitive explanation

For “Sinusoidal signal”: the RMS phasor rotates at ω; its projection is the sinusoid and Z = R + jX summarizes the element.

Worked example

For

v=10\cos(100t+30^\circ)\,\mathrm V

V_p=10\,\mathrm V

\omega=100\,\mathrm{rad/s}

and

\phi=30^\circ

Common mistakes

mixing peak with RMS
using jωL with f in hertz and no 2π
dropping the sign of −j/(ωC)

Frequently asked questions

What must be checked before using the Sinusoidal signal relation?: Work in RMS, convert f to ω=2πf and keep reactance signs.

Also known as

RMS phasor, impedance, reactance, admittance, sinusoidal steady state

Conventions

V, rad/s, Ω or S according to the left-hand side

Last reviewed: 2026-09-19

Found an error? Contact us.

Related formulas

6. AC and phasors

Sinusoidal signal

In 6. AC and phasors

Formula

v(t)=V_p\cos(\omega t+\phi)

Detail

The sinusoid v(t)=Vp cos(ωt+φ) is the projection of the rotating phasor.

Explore the idea

Variables

$V_p$ peak (V)
$V_{\mathrm{rms}}$ RMS (V)
$\omega$ rad/s
$f$ Hz
$\phi$ rad
$Z,X$ Ω
$Y$ S.

Conditions

Sinusoidal steady state; RMS phasors unless a peak is stated.

Intuitive explanation

For “Sinusoidal signal”: the RMS phasor rotates at ω; its projection is the sinusoid and Z = R + jX summarizes the element.

Worked example

For

v=10\cos(100t+30^\circ)\,\mathrm V

V_p=10\,\mathrm V

\omega=100\,\mathrm{rad/s}

and

\phi=30^\circ

Common mistakes

mixing peak with RMS
using jωL with f in hertz and no 2π
dropping the sign of −j/(ωC)

Frequently asked questions

What must be checked before using the Sinusoidal signal relation?: Work in RMS, convert f to ω=2πf and keep reactance signs.

Also known as

RMS phasor, impedance, reactance, admittance, sinusoidal steady state

Conventions

V, rad/s, Ω or S according to the left-hand side

Last reviewed: 2026-09-19

Found an error? Contact us.

Sinusoidal signal

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Related topics

Conventions

Related formulas

Sinusoidal signal

Tags

Detail

Explore the idea

Variables

Conditions

Intuitive explanation

Worked example

Common mistakes

Frequently asked questions

Also known as

Related topics

Conventions

Related formulas