Two coils have a mutual inductance 0-005 H- The current changes in the first coil according to the equation I-im sin - t where im-10 A and - -100 - rad s-1 - The maximum value of the emf induced in the second coil is

E=μ dI/dt d/dt(I_m sin ω t)=I_m ω cos ω t dI/dtis maximum ⇒ cos ω t=1 ⇒dI/dt=I_m ω e= μ(I_m ω) e =0.005 × 10 × 100 π = 5 π (maximum value of emf) nbsp; ...

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Byju's Answer

Standard XII

Physics

LC Oscillation

Two coils hav...

Question

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation $I = i_{m} s i n ω t w h e r e i_{m} = 10 A a n d ω = 100 π r a d s^{- 1}$ . The maximum value of the emf induced in the second coil is

$π$

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$2 π$

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$4 π$

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$5 π$

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Solution

The correct option is D
$5 π$

$e = \frac{μ d I}{d t} \frac{d}{d t} (I_{m} s i n ω t) = I_{m} ω c o s ω t$

$\frac{d I}{d t} is maximum$
$\Rightarrow c o s ω t = 1 \Rightarrow \frac{d I}{d t} = I_{m} ω$
$e = μ (I_{m} ω)$
$e = 0.005 \times 10 \times 100 π = 5 π (maximum value of emf)$

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Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation I=im sin ωt where im=10 A and ω=100π rad s−1 . The maximum value of the emf induced in the second coil is

The correct option is D 5π e=μdIdt ddt(Im sin ωt)=Imωcos ωt dIdtis maximum ⇒cosωt=1⇒dIdt=Imω e=μ(Imω) e=0.005×10×100π=5π (maximum value of emf)

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation $I = i_{m} s i n ω t w h e r e i_{m} = 10 A a n d ω = 100 π r a d s^{- 1}$ . The maximum value of the emf induced in the second coil is

The correct option is D
$5 π$

$e = \frac{μ d I}{d t} \frac{d}{d t} (I_{m} s i n ω t) = I_{m} ω c o s ω t$

$\frac{d I}{d t} is maximum$
$\Rightarrow c o s ω t = 1 \Rightarrow \frac{d I}{d t} = I_{m} ω$
$e = μ (I_{m} ω)$
$e = 0.005 \times 10 \times 100 π = 5 π (maximum value of emf)$