Three resistances of magnitude R each are con | vedclass

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

Question

(B) The area of an equilateral triangle of side $a$ is $A = \frac{\sqrt{3}}{4} a^2$.The magnetic flux $\phi$ through the triangle is $\phi = B \cdot A

Vedclass · Accepted Answer

$\left( \frac{a^2 \lambda}{6 R} B_0 \right) e^{-\lambda t}$

Vedclass · Answer

(B) The area of an equilateral triangle of side $a$ is $A = \frac{\sqrt{3}}{4} a^2$.The magnetic flux $\phi$ through the triangle is $\phi = B \cdot A = (B_0 e^{-\lambda t}) \left( \frac{\sqrt{3}}{4} a^2 \right)$.According to Faraday's law,the induced electromotive force $(EMF)$ is $\varepsilon = -\frac{d\phi}{dt} = -\frac{d}{dt} \left( B_0 e^{-\lambda t} \frac{\sqrt{3}}{4} a^2 \right) = B_0 \lambda e^{-\lambda t} \frac{\sqrt{3}}{4} a^2$.The three resistors $R$ are connected in series in the loop,so the total resistance is $R_{eq} = 3R$.The induced current $I$ is given by $I = \frac{\varepsilon}{R_{eq}} = \frac{B_0 \lambda e^{-\lambda t} \frac{\sqrt{3}}{4} a^2}{3R} = \frac{\sqrt{3} a^2 \lambda B_0 e^{-\lambda t}}{12R} = \frac{a^2 \lambda B_0 e^{-\lambda t}}{4\sqrt{3} R}$.Comparing this with the options,the correct expression is $\left( \frac{a^2 \lambda}{4\sqrt{3} R} B_0 \right) e^{-\lambda t}$.

Three resistances of magnitude $R$ each are connected in the form of an equilateral triangle of side $a$. The combination is placed in a magnetic field $B = B_0 e^{-\lambda t}$ perpendicular to its plane. The induced current in the circuit is given by:

Similar Questions

In the following figure,the magnet is moved towards the coil with a speed $v$ and the induced $emf$ is $e$. If the magnet and the coil recede away from one another,each moving with speed $v$,the induced $emf$ in the coil will be: (Assume the separation in both cases is the same)

$A$ magnet is moved towards a stationary coil with speed $V$. The induced e.m.f. in the coil is $e$. If the magnet and the coil move away from one another,each moving with speed $V$,then the induced e.m.f. in the coil is:

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

The graph shows the variation in magnetic flux $\phi(t)$ with time through a coil. Which of the statements given below is not correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module