In a L-R circuit discharging current is given by I - I0 e-t- - where - is the time constant of the circuit find the rms current for the period t - 0 to t - -

RMS value over a time τ is defined as: I_rms = √(∫_0^τ I^2 dtτ) I_rms = √(∫_0^τ I_o^2 e^ 2t/τ dtτ) I_rms = √(I_o^2 2 e^ 2t/τ|_0^τ) I_rm ...

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Byju's Answer

Standard XII

Physics

Energy Stored in an Inductor

In a L-R ci...

Question

In a $L - R$ circuit discharging current is given by $I = I_{0} e^{- t / τ}$ where $τ$ is the time constant of the circuit find the rms current for the period $t = 0$ to $t = τ$ .

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Solution

RMS value over a time $τ$ is defined as:
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I^{2} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I_{o}^{2} e^{- 2 t / τ} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{I_{o}^{2}}{- 2} e^{- 2 t / τ} |_{0}^{τ}}$
$I_{r m s} = I_{o} \sqrt{\frac{1 - e^{- 2}}{2}}$

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In a L−R circuit discharging current is given by I=I0e−t/τ where τ is the time constant of the circuit find the rms current for the period t=0 to t=τ.

RMS value over a time τ is defined as:Irms= ⎷∫τ0I2dtτIrms= ⎷∫τ0I2oe−2t/τdtτIrms= ⎷I2o−2e−2t/τ|τ0Irms=Io√1−e−22

In a $L - R$ circuit discharging current is given by $I = I_{0} e^{- t / τ}$ where $τ$ is the time constant of the circuit find the rms current for the period $t = 0$ to $t = τ$ .

RMS value over a time $τ$ is defined as:
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I^{2} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I_{o}^{2} e^{- 2 t / τ} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{I_{o}^{2}}{- 2} e^{- 2 t / τ} |_{0}^{τ}}$
$I_{r m s} = I_{o} \sqrt{\frac{1 - e^{- 2}}{2}}$