Electromagnetic Induction and Alternating Current 7 Question 10
10. A short-circuited coil is placed in a time varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled (four times) and the wire radius halved, the electrical power dissipated would be
$(2002,2 M)$
(a) halved
(b) the same
(c) doubled
(d) quadrupled
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Answer:
Correct Answer: 10. (d)
Solution:
- Power, $P=e^{2} / R$
Here, $e=$ induced emf $=-\frac{d \varphi}{d t}$ where, $\varphi=N B A$
$$ e=-N A \frac{d B}{d t} $$
Also, $\quad R \propto \frac{l}{r^{2}}$
where, $R=$ resistance, $r=$ radius, $l=$ length.
$$ \therefore \quad P \propto N^{2} r^{2} \Rightarrow \therefore \frac{P _2}{P _1}=4 $$
