The charge flown through a circuit in the time interval between t and t-d t is given by dq - e - t - - dt- where T is a constant- Find the toatal charge flown through the circuit t -0 to t - TA- -1-e-1B- -1-1-2C- -1-1e-eD- None of these

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The charge fl...

Question

The charge flown through a circuit in the time interval between t and t+dt is given by $d q = e^{- t / τ} d t$ , where $τ$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $τ$

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None of these

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Solution

The correct option is B

Solution: The total charge flown is the sum of all the dq's for t varying from t = 0 to $t = t_{0}$ . Thus, the total charge flown is

$Q = τ \int 0 e^{- t / t} d t$

= $[\frac{e^{- t / τ}}{- 1 / τ}]_{0}^{τ} = τ ⟮ 1 - \frac{1}{e} ⟯$

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The charge flown through a circuit in the time interval between t and t+dt is given by $d q = e^{- t / τ} d t$ , where $τ$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $τ$

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The charge flown through a circuit in the time interval between t and t+dt is given by dq=e−t/τdt, where τ is a constant. Find the toatal charge flown through the circuit t = 0 to t = τ

The correct option is B Solution: The total charge flown is the sum of all the dq's for t varying from t = 0 to t=t0. Thus, the total charge flown is Q=τ∫0e−t/tdt =[e−t/τ−1/τ]τ0=τ⟮1−1e⟯

The charge flown through a circuit in the time interval between t and t+dt is given by $d q = e^{- t / τ} d t$ , where $τ$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $τ$

The correct option is B

Solution: The total charge flown is the sum of all the dq's for t varying from t = 0 to $t = t_{0}$ . Thus, the total charge flown is

$Q = τ \int 0 e^{- t / t} d t$

= $[\frac{e^{- t / τ}}{- 1 / τ}]_{0}^{τ} = τ ⟮ 1 - \frac{1}{e} ⟯$