SATHEE: Electromagnetic Induction and Alternating Current 3 Question 4

Electromagnetic Induction and Alternating Current 3 Question 4

####4. A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 , keeping the number of turns of the coil per unit length of the frame the same, then the self-inductance of the coil

(Main 2019, 11 Jan II)

(a) increases by a factor of 3 .

(b) decreases by a factor of $9 \sqrt{3}$ .

(d) decreases by a factor of 9 .

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Answer:

Correct Answer: 4. (c)

Solution:

Self-inductance of a coil is given by the relation

$L = μ_{0} n^{2} A \cdot l$

where, $n$ is number of turns per unit length. Shape of the wooden frame is equilateral triangle.

$∴$ Area of equilateral triangle,

$A = \frac{\sqrt{3}}{4} a^{2}$

(where, $a$ is side of equilateral triangle)

$∴$ Self-inductance, $L = μ_{0} n^{2} \frac{\sqrt{3}}{4} a^{2} \cdot l$

Here, $l = 3 a \times N$ (where, $N$ is total number of turns) $∴ L = μ_{0} n^{2} \frac{\sqrt{3}}{4} a^{2} \times 3 a N$ or $L \propto a^{3}$

When each side of frame is increased by a factor 3 keeping the number of turns per unit length of the frame constant.

Then,

$a^{'} = 3 a$

$\begin{array}{ll} ∴ & L^{'} \propto {(a^{'})}^{3} or L^{'} \propto (3 a)^{3} \\ or & L^{'} \propto 27 a^{3} or L^{'} = 27 L \end{array}$

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Electromagnetic Induction and Alternating Current 3 Question 4

Answer:

इंजीनियरिंग की तैयारी

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Electromagnetic Induction and Alternating Current 3 Question 4

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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