First slide

Inductance

Question

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $ϕ$ linked with the primary coil is given by $ϕ = ϕ_{0} + 4 t$ , where $ϕ$ is in weber, t is time in second and $ϕ_{0}$ is a constant, the output voltage across the secondary coil is :

Moderate

A

90 V
B

120 V
C

220 V
D

30 V

Solution

Induced emf in primary coil $E_{p} = \frac{dϕ}{dt} = \frac{d}{dt} (ϕ_{0} + 4 t) = 4 V$
Induced emf in secondary coil
$\frac{E_{s}}{E_{p}} = \frac{N_{s}}{N_{p}} \Rightarrow \frac{E_{s}}{4} = \frac{1500}{50} \Rightarrow E_{s} = 120 V$

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