SATHEE: Electro Magnetic Induction And Alternating Currents Question 337

Electro Magnetic Induction And Alternating Currents Question 337

Question: is a circular loop of radius r and resistance R. A variable magnetic field of induction $B = B_{0} e^{- t}$ is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

Options:

A) $\frac{B_{0}^{2} π r^{2}}{R}$

B) $\frac{B_{0} 10 r^{3}}{R}$

C) $\frac{B_{0}^{2} π^{2} r^{4} R}{5}$

D) $\frac{B_{0}^{2} π^{2} r^{4}}{R}$

Show Answer

Answer:

Correct Answer: D

Solution:

$P = \frac{e^{2}}{R}; e = - \frac{d}{d t} (B A) = A \frac{d}{d t} (B_{o} e^{- t}) = A B_{o} e^{- t}$
$\Rightarrow P = \frac{1}{R} {(A B_{o} e^{- t})}^{2} = \frac{A^{2} B_{o}^{2} e^{- 2 t}}{R}$ At the time of starting t = 0 so $P = \frac{A^{2} B_{o}^{2}}{R}$
$\Rightarrow P = \frac{{(π r^{2})}^{2} B_{o}^{2}}{R} = \frac{B_{o}^{2} π^{2} r^{4}}{R}$

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Electro Magnetic Induction And Alternating Currents Question 337

Question: is a circular loop of radius r and resistance R. A variable magnetic field of induction B=B0e−t is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

Options:

Answer:

Solution:

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Question: is a circular loop of radius r and resistance R. A variable magnetic field of induction $B = B_{0} e^{- t}$ is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to