SATHEE: Electro Magnetic Induction And Alternating Currents Question 458

Electro Magnetic Induction And Alternating Currents Question 458

Question: a conducting loop consisting of half circle of area $A = 0.06, m^{2}$ and three straight segments. The half circle lies in a uniform changing magnetic field $B = 4 r^{2} + 2 t + 5$ (SI unit), where t is the time in second. An ideal battery E=2V is connected as shown and the total resistance of the wire is $2 Ω$ . The net current in the loop is at t=5 second is:

Options:

A) 1A

B) 1.5A

C) 0.26A

D) 0.10A

Show Answer

Answer:

Correct Answer: C

Solution:

$e_{i n d} = \frac{d ϕ}{d t} = \frac{d}{d t} (B A) = A \frac{d B}{d t}$

$= A \frac{d}{d t} (4 t^{2} + 2 t + 5) = A (8 t + 2) = 0.06 (8 t + 2)$ =2.52 at t=5

$\frac{i = 2 - e_{i n d}}{2} = 0.26, A$

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Electro Magnetic Induction And Alternating Currents Question 458

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