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The primary and secondary coil of a transformer have 50 and 1500 turns respectively. If the magnetic flux ϕ linked with the primary coil is given by ϕ = ϕ₀ + 4t, where ϕ is in webers, t is time in seconds and ϕ₀ is a constant, the output voltage across the secondary coil is

1. 120 volts
2. 220 volts
3. 30 volts
4. 90 volts

Correct answer: 120 volts

Solution

The EMF induced in the primary coil is given by Faraday's law as E₁ = -N₁(dϕ/dt). Here, dϕ/dt = 4 Wb/s and N₁ = 50, so E₁ = -50 × 4 = -200 V. The transformer equation relates the primary and secondary voltages as E₂/E₁ = N₂/N₁. Substituting N₂ = 1500 and N₁ = 50, we get E₂ = (1500/50) × 200 = 120 V. Thus, the output voltage is 120 V.

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