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Question #43930

Difficulty: 8/10 | 🟢 Free

The Question

A non-ohmic semiconductor device has a voltage-current characteristic given by $I = k V^2$ for $V > 0$ , where $k = 0.25 \text{ A V}^{-2}$ . The device is connected in series with a cell of internal resistance $r = 2.0 \ \Omega$ . The electromotive force (EMF) of the cell, $E$ , varies with temperature $T$ according to the relation $E(T) = E_0 + \alpha (T - T_0)$ , where $E_0 = 12.0 \text{ V}$ and the temperature coefficient $\alpha = 50 \text{ mV } ^\circ\text{C}^{-1}$ . What is the rate of change of the circuit current with respect to temperature, $\frac{dI}{dT}$ , at $T = T_0$ ?

Options

A.
$20 \text{ mA } ^\circ\text{C}^{-1}$
B.
$16.7 \text{ mA } ^\circ\text{C}^{-1}$
C.
$25 \text{ mA } ^\circ\text{C}^{-1}$
D.
$100 \text{ mA } ^\circ\text{C}^{-1}$

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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

Cell EMF vs Terminal Voltage|Dynamic Resistance (AC Resistance)|Calculus (Differentiation)

Why This Question Is Tricky

Common Mistakes

This question tests the ability to perform small-signal (dynamic) analysis on a non-linear circuit using Kirchhoff's Laws.

The primary trap exploits the 'standard intuition' of Ohm's Law, where students often incorrectly use the static resistance ( $R_s = V/I = 1.0 \ \Omega$ ) instead of the dynamic resistance ( $r_d = dV/dI = 0.5 \ \Omega$ ) when evaluating differential changes in the circuit.

By differentiating the KVL equation, it becomes clear that the total effective resistance to small changes in EMF is $r + r_d$ , not $r + R_s$ .

Using the static resistance leads directly to the incorrect option B.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Current Electricity - Class 12
Concept	Cell EMF vs Terminal Voltage
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free