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Question
Two coils C1 and C2 are placed close to each other. The magnetic flux Φ2 linked with coil C2 varies with the current I1 flowing in coil C1 as shown in the figure. Find
- The mutual inductance of the arrangement, and
- The rate of change of current `((dI_1)/(dt))` will induce an emf of 100V in coil C2.
Solution
- Φ2 = magnetic flux linked with coil C2.
I1 = current passes in coil C1.
Lets no. of turns in coil C1 be N1.
No. of turns in coil C2 be N2.
According to Faraday's law,
`E_"ind" = (dphi)/(dt)`
`E_{21} = -N_2(dphi_2)/(dt)`
`E_21 = -N_2d/dt(vecB . vecA)`
`N_2phi_2 prop I_1`
`N_2phi_2 = M_21I_1`
M21 is called mutual inductance.
`M_21 = (N_2phi_2)/I_1` - Induced emf (E) = `-L(dI)/(dt)`
`(dI)/(dt) = E/(-L)`
`(dI_1)/(dt) = -100(1/L)`
Here, L is the inductance of the coil C2.
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