SATHEE: Electromagnetic Induction and Alternating Current 1 Question 15

Electromagnetic Induction and Alternating Current 1 Question 15

15. A rectangular frame $A B C D$ , made of a uniform metal wire, has a straight connection between $E$ and $F$ made of the same wire, as shown in figure. $A E F D$ is a square of side $1 m$ and $E B$ $= F C = 0.5 m$ . The entire circuit is placed in a steadily increasing uniform magnetic field directed into the plane of the paper and normal to it.

The rate of change of the magnetic field is $1 T / s$ . The resistance per unit length of the wire is $1 Ω / m$ . Find the magnitudes and directions of the currents in the segments $A E$ , $B E$ and $E F$ .

(1993, 5M)

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Answer:

Correct Answer: 15. $\frac{7}{22} A (E$ to $A), \frac{6}{22} A (B$ to $E), \frac{1}{22} A (F$ to $E)$

Solution:

Induced emf in two loops $A E F D$ and $E B C F$ would be

$e_{1} = \frac{d φ_{1}}{d t} = S_{1} \frac{d B}{d t} = (1 \times 1) (1) V = 1 V$

Similarly, $e_{2} = \frac{d φ_{2}}{d t} = S_{2} \frac{d B}{d t} = (0.5 \times 1) (1) V = 0.5 V$

Now, since the magnetic field is increasing, the induced current will produce the magnetic field in $U$ direction. Hence, $e_{1}$ and $e_{2}$ will be applied as shown in the figure.

Kirchhoff’s first law at junction $F$ gives

$i_{1} = i + i_{2}$

Kirchhoff’s second law in loop FEADF gives

$3 i_{1} + i = 1$

Kirchhoff’s second law in loop $F E B C F$ gives

$2 i_{2} - i = 0.5$

Solving Eqs. (i), (ii) and (iii), we get

$\begin{aligned} i_{1} & = \frac{7}{22} A and i_{2} = \frac{6}{22} A \\ and i & = (1 / 22) A \end{aligned}$

Therefore, current in segment $A E$ is (7/22) A from $E$ to $A$ , current in segment $B E$ is $6 / 22 A$ from $B$ to $E$ and current in segment $E F$ is (1/22) A from $F$ to $E$ .

Electromagnetic Induction and Alternating Current 1 Question 15

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Electromagnetic Induction and Alternating Current 1 Question 15

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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