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Question
Derive the equation for a transformer.
Solution
Let NP and Ns be the number of turns of the primary and secondary coils. Let Φ be the magnetic flux linked per turn.
Φp = NpΦ
= Total magnetic flux linked with the primary coil at certain instant,
Φs = NsΦ
= Total magnetic flux linked with the secondary coil at a certain instant.
By Faraday and Lenz's laws,
Induced emf in the primary coil (ep) is given by
`e_p = -(dphi_p)/dt`
= `-N_p(dphi)/dt` ...(i)
emf induced in the secondary coil (es) is
`e_s = -(dphi_s)/dt`
= `-N_s(dphi)/dt` ...(ii)
Dividing equation (ii) by equation (i),
`e_s/e_p = N_s/N_p` ...(iii)
The ratio `N_s/N_p` is called the turn ratio.
For an ideal transformer,
Input power = Output Power
epIp = esIs
`e_s/e_p = I_p/I_s` ...(iv)
From equations (iii) and (iv),
`e_s/e_p = N_s/N_p = I_p/I_s` ...(v)
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