SATHEE: Electro Magnetic Induction And Alternating Currents Question 308

Electro Magnetic Induction And Alternating Currents Question 308

Question: An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time $t = \infty$ and at t = 1 second is [MP PMT 1994]

Options:

A) $\frac{e^{1 / 2}}{e^{1 / 2} - 1}$

B) $\frac{e^{2}}{e^{2} - 1}$

C) $1 - e^{- 1}$

D) $e^{- 1}$

Show Answer

Answer:

Correct Answer: B

Solution:

$i = i_{0} (1 - e^{- R t / L})$

$i_{0} = \frac{E}{R}$ (Steady current)

when $t = \infty$

$i_{\infty} = \frac{E}{R} (1 - e^{- \infty}) = \frac{5}{10} = 1.5$

$i_{1} = 1.5 (1 - e^{- R / L}) = 1.5 (1 - e^{- 2})$

Þ $\frac{i_{\infty}}{i_{1}} = \frac{1}{1 - e^{- 2}} = \frac{e^{2}}{e^{2} - 1}$

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Electro Magnetic Induction And Alternating Currents Question 308

Question: An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t=∞ and at t = 1 second is [MP PMT 1994]

Options:

Answer:

Solution:

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Question: An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time $t = \infty$ and at t = 1 second is [MP PMT 1994]