An emf of <math> <mn>20</mn> <mtext> </mtext> <mi mathvariant="normal">V</mi> </math> is applied at time <math> <mi mathvariant="normal">t</mi> <mo>=</mo> <mn>0</mn> </math> to a circuit containing in series <math> <mn>10</mn> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">H</mi> </math> inductor and <math> <mn>5</mn> <mi mathvariant="normal">Ω</mi> </math> resistor. The ratio of the currents at time <math> <mi>t</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> </math> and at <math> <mi>t</mi> <mo>=</mo> <mn>40</mn> <mtext> </mtext> <mi mathvariant="normal">s</mi> </math> is close to: (take <math> <mfenced open="" separators="|"> <mrow> <mrow> <msup> <mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <mn>7.389</mn> </mrow> </mrow> </mfenced> </math>

i = V r 1 - e - R t / L = 4 1 - e - 500 t At t = ∞ i 1 = 4 A at t = 40 s i 2 = 4 1 - e - 20000 = 4 1 - 1 e 2 10000 = 4 1 - 1 ( 7.389 ) 10000 i 1 i 2 is slightly greater than 1 .

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Alternating Current Overview Physics Alternating Current Physics Class 12th

An emf of $20 V$ is applied at time $t = 0$ to a circuit containing in series $10 m H$ inductor and $5 Ω$ resistor. The ratio of the currents at time $t = \infty$ and at $t = 40 s$ is close to: (take $e^{2} = 7.389)$

Option 1 -

1.06

Option 2 -

0.84

Option 3 -

1.46

Option 4 -

1.15

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

$\begin{array}{r} i & = \frac{V}{r} (1 - e^{- R t / L}) \\ = 4 (1 - e^{- 500 t}) \end{array}$

At $t = \infty$

$i_{1} = 4 A$

at $t = 40 s$

$i_{2} = 4 (1 - e^{- 20000})$

= 4 [1 - \frac{1}{{(e^{2})}^{10000}}]

= 4 [1 - \frac{1}{(7.389)^{10000}}]

\frac{i_{1}}{i_{2}}

is slightly greater than 1 .

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An emf of $20 V$ is applied at time $t = 0$ to a circuit containing in series $10 m H$ inductor and $5 Ω$ resistor. The ratio of the currents at time $t = \infty$ and at $t = 40 s$ is close to: (take $e^{2} = 7.389)$

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An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 m H inductor and 5 Ω resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to: (take e 2 = 7.389

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An emf of $20 V$ is applied at time $t = 0$ to a circuit containing in series $10 m H$ inductor and $5 Ω$ resistor. The ratio of the currents at time $t = \infty$ and at $t = 40 s$ is close to: (take $e^{2} = 7.389)$