AP EAMCET · PHYSICS · Electromagnetic Induction

An emf of $15 V$ is applied to a circuit containing $5 H$ inductance and $10 Ω$ resistance. The ratio of currents at time $t = \infty$ and $t = 1$ s after closing the switch is:

A $\frac{e}{e^{2} - 1}$
B $\frac{e^{2}}{e - 1}$
C $\frac{e}{1 - e^{2}}$
D $\frac{e^{2}}{e^{2} - 1}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{e^{2}}{e^{2} - 1}$

Step-by-step Solution

Detailed explanation

Given: The inductance L=5 H, resistance R=10 Ω and emf applied V=15 V. The time constant for LR constant is given by, τL=LR=12 s The current in the LR circuit is given by, i=i01-e-t/τL; where i0=VR is the maximum current at t=∞. The ratio…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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An emf of 15 V is applied to a circuit containing 5 H inductance and 10 Ω resistance. The ratio of currents at time t=∞ and t=1 s after closing the switch is:

Step-by-step Solution

An emf of $15 V$ is applied to a circuit containing $5 H$ inductance and $10 Ω$ resistance. The ratio of currents at time $t = \infty$ and $t = 1$ s after closing the switch is: