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Physics - EMI/AC Question with Solution | TestHub

PhysicsEMI/ACL-R circuitEasy2 minPYQ_2020

PhysicsEasynumerical

A coil having inductance $L$ and resistance $R$ is connected to a battery of emf $ε$ at $t = 0$ . If $t_{1}$ and $t_{2}$ are the time for $90 %$ and $99 %$ completion of the current growth in the circuit, then $\frac{t_{1}}{t_{2}}$ will be-

Answer:

0.50

Solution:

$I = I_{0} (1 - e^{- \frac{t}{τ}})$

$\frac{9}{10} I_{0} = I_{0} (1 - e^{- \frac{t_{1}}{τ}})$

$\Rightarrow e^{- \frac{t_{1}}{τ}} = \frac{1}{10}$

$\Rightarrow e^{\frac{t_{1}}{τ}} = 10$

$\Rightarrow t_{1} = τ ln 10$

and $\frac{99}{100} I_{0} = I_{0} (1 - e^{- \frac{t_{2}}{τ}})$

$\Rightarrow e^{- \frac{t_{2}}{τ}} = \frac{1}{100}$

$\Rightarrow t_{2} = τ ln 100 = 2 τ ln 10$

$\Rightarrow \frac{t_{1}}{t_{2}} = 0.5$

Subject:PhysicsTopic:EMI/ACSubtopic:L-R circuit

⏱ 2mℹ️ Source: PYQ_2020

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