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 ...

255

You visited us 255 times! Enjoying our articles? Unlock Full Access!

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 $t = τ$ .

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. In a LR 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 from the period

t = 0

t = τ

Q. The current in a discharging LR circuit is given by i = i₀e^−t^/τ , where τ is the time constant of the circuit. Calculate the rms current for the period t = 0 to t = τ.

Q. The current decaying in a circuit has a function

i = I_{0} e^{- t / τ}

where

τ

is the time constant of the circuit. Find

r m s

value of the current for the period

t = 0 to t = τ

The current in a discharging LR circuit is given by $i = i_{0} e - t τ$ where \tau is the time constant of the circuit. Calculate the rms current for the period t = 0 to $t = τ$ .

Q. The electric current in a circuit is given by

i = i_{0} (\frac{t}{τ})

for some time. Then the

r . m . s .

current for the period

t = 0

t = τ

Join BYJU'S Learning Program

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:
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I^{2} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{\int_{0}^{τ} I_{o}^{2} e^{- 2 t / τ} d t}{τ}}$
$I_{r m s} = \sqrt{\frac{I_{o}^{2}}{- 2} e^{- 2 t / τ} |_{0}^{τ}}$
$I_{r m s} = I_{o} \sqrt{\frac{1 - e^{- 2}}{2}}$