SATHEE: Electromagnetic Induction and Alternating Current 1 Question 3

Electromagnetic Induction and Alternating Current 1 Question 3

3. The self-induced emf of a coil is $25 V$ . When the current in it is changed at uniform rate from $10 A$ to $25 A$ in $1 s$ , the change in the energy of the inductance is

(Main 2019, 10 Jan II)

(a) $437.5 J$

(b) $740 J$

(d) $540 J$

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Answer:

Correct Answer: 3. (a)

Solution:

Energy stored in an inductor of inductance $L$ and current $I$ is given by

$E = \frac{1}{2} L I^{2}$

When current is being changed from $I_{1}$ to $I_{2}$ , change in energy will be

$Δ E = E_{2} - E_{1} = \frac{1}{2} L I_{2}^{2} - \frac{1}{2} L I_{1}^{2}$

As $I_{1}$ and $I_{2}$ are given, we need to find value of $L$ .

Now, induced emf in a coil is

$ε = L \frac{d I}{d t}$

Here,

$ε = 25 V$

$d I = I_{2} - I_{1} = (25 - 10) = 15 A and d t = 1 s$

$\Rightarrow 25 = L \times \frac{15}{1} or L = \frac{25}{15} = 5 / 3 H$

Putting values of $L, I_{1}$ and $I_{2}$ in Eq. (i), we get

$Δ E = \frac{1}{2} \times \frac{5}{3} \times [25^{2} - 10^{2}] = \frac{1}{2} \times \frac{5}{3} \times 525 Δ E = 437.5 J$

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Electromagnetic Induction and Alternating Current 1 Question 3

3. The self-induced emf of a coil is $25 V$ . When the current in it is changed at uniform rate from $10 A$ to $25 A$ in $1 s$ , the change in the energy of the inductance is

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

Electromagnetic Induction and Alternating Current 1 Question 3

3. The self-induced emf of a coil is 25V. When the current in it is changed at uniform rate from 10A to 25A in 1s, the change in the energy of the inductance is

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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3. The self-induced emf of a coil is $25 V$ . When the current in it is changed at uniform rate from $10 A$ to $25 A$ in $1 s$ , the change in the energy of the inductance is