Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I=I0sin (ω t), where I0=10A and ω =100π rad s- 1. The maximum value of emf in the second coil is

Question

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I=I0sin (ω t), where I0=10A and ω =100π rad s- 1. The maximum value of emf in the second coil is (A) 2π  (B) 5π  (C) π  (D) 4π

Tardigrade Admin · Accepted Answer

emf, induced in second coil e=M (d I/d t) ⇒ e=M (d/d t) I0 sin ω t=M I0 ω cos ω t ⇒ e=0.005 × 10 × 100 π cos ω t ⇒ e=5 π cos ω t, e max =5 π (emf is maximum for cos ω t=1 )

Q. Two coils have a mutual inductance $0.005 H .$ The current changes in the first coil according to equation $I = I_{0} s in (ω t),$ where $I_{0} = 10 A$ and $ω = 100 π r a d s^{- 1} .$ The maximum value of emf in the second coil is

$2 π$

$5 π$

$π$

$4 π$

emf, induced in second coil $e = M \frac{d I}{d t}$
$\Rightarrow e = M \frac{d}{d t} I_{0} sin ω t = M I_{0} ω cos ω t$
$\Rightarrow e = 0.005 \times 10 \times 100 π cos ω t$
$\Rightarrow e = 5 π cos ω t, e_{m a x} = 5 π$
(emf is maximum for $cos ω t = 1$ )

Q. Two coils have a mutual inductance 0.005H. The current changes in the first coil according to equation I=I0​sin(ωt), where I0​=10A and ω=100πrads−1. The maximum value of emf in the second coil is

2π

5π

π

4π

emf, induced in second coil e=MdtdI​ ⇒e=Mdtd​I0​sinωt=MI0​ωcosωt ⇒e=0.005×10×100πcosωt ⇒e=5πcosωt,emax​=5π (emf is maximum for cosωt=1 )

Q. Two coils have a mutual inductance $0.005 H .$ The current changes in the first coil according to equation $I = I_{0} s in (ω t),$ where $I_{0} = 10 A$ and $ω = 100 π r a d s^{- 1} .$ The maximum value of emf in the second coil is

$2 π$

$5 π$

$π$

$4 π$

emf, induced in second coil $e = M \frac{d I}{d t}$
$\Rightarrow e = M \frac{d}{d t} I_{0} sin ω t = M I_{0} ω cos ω t$
$\Rightarrow e = 0.005 \times 10 \times 100 π cos ω t$
$\Rightarrow e = 5 π cos ω t, e_{m a x} = 5 π$
(emf is maximum for $cos ω t = 1$ )