SATHEE: Electro Magnetic Induction And Alternating Currents Question 455

Electro Magnetic Induction And Alternating Currents Question 455

Question: Magnetic flux linked with a stationary loop of resistance R varies with respect to time during the time period T as follows: $ϕ = a t (T - t)$ The amount of heat generated in the loop during that time (inductance of the coil is negligible) is

Options:

A) $\frac{a T}{3 R}$

B) $\frac{a^{2} T^{2}}{3 R}$

C) $\frac{a^{2} T^{2}}{R}$

D) $\frac{a^{2} T^{3}}{3 R}$

Show Answer

Answer:

Correct Answer: D

Solution:

Given that $ϕ = a t (T - t)$

Induced emf, $E = \frac{d ϕ}{d t} = \frac{d}{d t} [a t (T - t)]$ = at $(0 - 1) + a (T - t) = a (T - 2 t)$

So, induced emf is also a function of time.

$∴$ Heat generated in time T is $H \int_{0}^{T} \frac{E^{2}}{R} d t = \frac{a^{2}}{R} \int_{0}^{T} {(T - 2 t)}^{2}$

$d t = \frac{a^{2} T^{3}}{3 R}$

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Electro Magnetic Induction And Alternating Currents Question 455

Question: Magnetic flux linked with a stationary loop of resistance R varies with respect to time during the time period T as follows: ϕ=at(T−t) The amount of heat generated in the loop during that time (inductance of the coil is negligible) is

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Question: Magnetic flux linked with a stationary loop of resistance R varies with respect to time during the time period T as follows: $ϕ = a t (T - t)$ The amount of heat generated in the loop during that time (inductance of the coil is negligible) is