The magnetic flux through a stationary loop w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic flux is given by $\phi = a t(T - t) = a T t - a t^2$.According to Faraday's law,the induced electromotive force $(EMF)$ is $\varepsil

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The magnetic flux is given by $\phi = a t(T - t) = a T t - a t^2$.According to Faraday's law,the induced electromotive force $(EMF)$ is $\varepsilon = -\frac{d\phi}{dt}$.$\varepsilon = -\frac{d}{dt}(a T t - a t^2) = -(a T - 2 a t) = 2 a t - a T$.The power dissipated in the loop is $P = \frac{\varepsilon^2}{R} = \frac{(2 a t - a T)^2}{R}$.The total heat generated $H$ in the interval $t = 0$ to $t = T$ is given by $H = \int_{0}^{T} P dt$.$H = \int_{0}^{T} \frac{(2 a t - a T)^2}{R} dt = \frac{1}{R} \int_{0}^{T} (4 a^2 t^2 - 4 a^2 T t + a^2 T^2) dt$.$H = \frac{a^2}{R} [\frac{4 t^3}{3} - 2 T t^2 + T^2 t]_{0}^{T}$.$H = \frac{a^2}{R} [\frac{4 T^3}{3} - 2 T^3 + T^3] = \frac{a^2}{R} [\frac{4 T^3 - 6 T^3 + 3 T^3}{3}] = \frac{a^2 T^3}{3 R}$.

The magnetic flux through a stationary loop with resistance $R$ varies during an interval of time $T$ as $\phi = a t(T - t)$. The heat generated during this time,neglecting the inductance of the loop,will be:

Similar Questions

Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

$DNA$ fingerprinting involves:

Breeding crops with higher levels of vitamins,minerals,and proteins is known as ..........

What is the term used to describe the variety in size, shape, structure, lifestyle, and other aspects of organisms living in different regions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module