The charge flown through a circuit in the time interval between t and t-dt is given by dq-e-t- dt- where - is a constant- Find the toatal charge flown through the circuit t - 0 to t - -

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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 = $τ$

$τ (\frac{1}{e} - 1)$

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$τ (1 - \frac{1}{e})$

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$τ (1 + \frac{1}{e})$

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None of these

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Solution

The correct option is B
$τ (1 - \frac{1}{e})$

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 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 τ(1−1e) 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
$τ (1 - \frac{1}{e})$

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

$Q = τ \int 0 e^{- t / t} d t$

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