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Question #42721

Difficulty: 8/10 | 🟢 Free

The Question

An ideal battery of EMF $E = 12 \text{ V}$ is connected in series with a switch $S$ and a resistor $R_1 = 2 \text{ }\Omega$ . The circuit then splits into two parallel branches that recombine and return to the battery. Branch 1 contains a resistor $R_2 = 4 \text{ }\Omega$ and an inductor $L = 4 \text{ H}$ in series. Branch 2 contains a single resistor $R_3 = 4 \text{ }\Omega$ . The switch $S$ is closed at $t = 0$ . At the specific instant when the total current drawn from the battery is $I = 2.5 \text{ A}$ , what is the rate of change of current $\frac{di_1}{dt}$ in Branch 1?

Options

A.
$1.0 \text{ A/s}$
B.
$0.5 \text{ A/s}$
C.
$1.75 \text{ A/s}$
D.
$2.25 \text{ A/s}$

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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

Ohm's Law Validity|Kirchhoff’s Junction Rule|Transient Current in RL Circuit

Why This Question Is Tricky

Common Mistakes

This question tests the application of Kirchhoff's laws in a transient RL circuit, specifically targeting the misconception that parallel branches with equal resistances must carry equal currents.

Students often incorrectly apply Ohm's Law algebraically ( $i_1 R_2 = i_2 R_3$ ) across the parallel branches, ignoring the induced back-EMF ( $L \frac{di}{dt}$ ) of the inductor.

By forcing the student to find the instantaneous branch currents using the purely resistive branch first, the problem demands a rigorous application of KVL and KCL, highlighting that Ohm's Law only governs the resistive components while the inductor's voltage is strictly differential.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Current Electricity - Class 12
Concept	Ohm's Law Validity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free