A circuit area 0.01 m2 is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 tesla to 1 tesla in 1 millisecond. If the resistance of the circuit is 2 Ω. The rate of heat evolved is

Question

A circuit area 0.01 m2 is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 tesla to 1 tesla in 1 millisecond. If the resistance of the circuit is 2 Ω. The rate of heat evolved is (A) 5 J/s (B) 50 J/s (C) 0.05 J/s (D) 0.5 J/s

Tardigrade Admin · Accepted Answer

Induced emf, e=(-dφ/dt) ⇒ e=(-(φ2-φ1)/t)=((0.01-0.02)/1×10-3) e=0.01×103=10 volt V=IR or (10/2)=I ∴ I=5 A Rate of heat evolved = I2R=(5)2×2 =25×2=50J/ s

Q. A circuit area $0.01 m^{2}$ is kept inside a magnetic field which is normal to its plane. The magnetic field changes from $2$ tesla to $1$ tesla in $1$ millisecond. If the resistance of the circuit is $2 Ω$ . The rate of heat evolved is

$5 J / s$

$50 J / s$

$0.05 J / s$

$0.5 J / s$

Induced emf, $e = \frac{- d ϕ}{d t}$
$\Rightarrow e = \frac{- ( ϕ _{2} - ϕ _{1} )}{t} = \frac{( 0.01 - 0.02 )}{1 \times 1 0 ^{- 3}}$
$e = 0.01 \times 1 0^{3} = 10$ volt
$V = I R$ or $\frac{10}{2} = I$
$∴ I = 5 A$
Rate of heat evolved $= I^{2} R = (5)^{2} \times 2$
$= 25 \times 2 = 50 J / s$

Q. A circuit area 0.01m2 is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 tesla to 1 tesla in 1 millisecond. If the resistance of the circuit is 2Ω. The rate of heat evolved is

5J/s

50J/s

0.05J/s

0.5J/s