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Question #42417

Difficulty: 8/10 | 🟢 Free

The Question

An ideal inductor of inductance $L = 2\text{ H}$ and a resistor of resistance $R = 5\ \Omega$ are connected in series to a DC voltage source of $V = 10\text{ V}$ and a switch. The switch is closed at $t = 0$ . Let $\tau$ be the inductive time constant of the circuit. What is the average current flowing through the circuit during the time interval $t = 0$ to $t = \tau$ ?

Options

A.
$\frac{2}{e}\text{ A}$
B.
1\text{ A}
C.
$2\left(1 - \frac{1}{e}\right)\text{ A}$
D.
$\left(1 - \frac{1}{e}\right)\text{ A}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Instantaneous vs Average|Transient Current in RL Circuit|Calculus: Integration

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between the time-averaged value of an exponential transient process and the arithmetic mean of its boundary values.

A common trap is assuming the average current over the first time constant is either half the steady-state current (yielding 1 A) or the instantaneous current evaluated exactly at t = au (yielding 2(1 - 1/e) A).

Students often bypass the calculus-based definition of an average, incorrectly applying linear approximations to non-linear exponential accumulations.

The correct approach requires rigorous integration, revealing that the average current is exactly V/(eR).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Instantaneous vs Average
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free