(A) Given: Number of turns $N = 50$,Area $A = 2.5 \ m^2$,Magnetic field $B = 0.3 \ T$,Angular velocity $\omega = 60 \ rad \ s^{-1}$,Resistance $R = 50

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(A) Given: Number of turns $N = 50$,Area $A = 2.5 \ m^2$,Magnetic field $B = 0.3 \ T$,Angular velocity $\omega = 60 \ rad \ s^{-1}$,Resistance $R = 500 \ \Omega$.The maximum induced $emf$ $(V_m)$ is given by the formula:$V_m = N B A \omega$$V_m = 50 \times 0.3 \times 2.5 \times 60$$V_m = 50 \times 0.3 \times 150 = 2250 \ V = 2.25 \ kV$.The maximum current $(I_m)$ is given by Ohm's law:$I_m = \frac{V_m}{R}$$I_m = \frac{2250 \ V}{500 \ \Omega} = 4.5 \ A$.Thus,the maximum induced $emf$ is $2.25 \ kV$ and the maximum current is $4.5 \ A$.

Class 12 Physics Electromagnetic Induction Dynamic EMI and Periodic EMI

Medium

The number of turns in the coil of an $AC$ generator are $50$ and its cross-sectional area is $2.5 \ m^2$. This coil is revolving in a uniform magnetic field of strength $0.3 \ T$ with a uniform angular velocity of $60 \ rad \ s^{-1}$. The resistance of the circuit comprising the coil is $500 \ \Omega$. The maximum induced $emf$ and maximum current produced in the generator are:

A
$2.25 \ kV, 4.5 \ A$
B
$2.25 \ kV, 2.5 \ A$
C
$4.5 \ kV, 4.5 \ A$
D
$3.25 \ kV, 2.5 \ A$

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Electromagnetic Induction

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Dynamic EMI and Periodic EMI

In a uniform magnetic field of induction $B$,a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$,the mean power generated per period of rotation is

DifficultAIEEE 2004

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Discuss the characteristics of the induced $emf$ in an $AC$ generator.

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In an $AC$ generator,a rectangular coil of $100$ turns each having area $14 \times 10^{-2} \, m^2$ is rotated at $360 \, rev/min$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0 \, T$. The maximum value of the emf produced will be $............ \, V$. (Take $\pi = \frac{22}{7}$)

EasyJEE MAIN 2023

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An elliptical loop having resistance $R$,semi-major axis $a$,and semi-minor axis $b$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$,the average power loss in the loop due to Joule heating is:

DifficultJEE MAIN 2020

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In a region of uniform magnetic induction $B = 10^{-2} \, T$,a circular coil of radius $r = 30 \, cm$ and resistance $R = \pi^2 \, \Omega$ is rotated about an axis which is perpendicular to the direction of $B$ and which forms a diameter of the coil. If the coil rotates at $200 \, rpm$,the amplitude of the alternating current induced in the coil is.....$mA$.

MediumAIPMT 1990

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Discuss the characteristics of the induced $emf$ in an $AC$ generator.

An elliptical loop having resistance $R$,semi-major axis $a$,and semi-minor axis $b$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$,the average power loss in the loop due to Joule heating is:

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