Question

A transformer consists of 340. Primary windings and 980. Secondary windings. Is the emf of the primary coil is 30.0V. What is the elf across the secondary coil?

O29.4

O34.7

O86.5

O59.6

Answer 1

Approximately
`86.5\; {\rm V}`.

Step-by-step explanation:

By Faraday's Law of Induction, the emf
`\epsilon` induced in a coil would be proportional to the number of turns
`N` in that coil and rate of change in magnetic flux through that coil
`d\Phi / d t`:

`\displaystyle \epsilon = -N\, (d\Phi)/(dt)`,

In a transformer, the rate of change
`d\Phi / d t` in magnetic flux is the same for both coils. Hence, the the emf induced in each coil would be directly proportional to the number of turns in each coil.

Let
`N_(P)` and
`N_(S)` denote the number of turns in the two coils. Let
`\epsilon_(P)` and
`\epsilon_(S)` denote the emf induced in the two coils.

`\displaystyle (\epsilon_(P))/(N_(P)) = (\epsilon_(S))/(N_(S))`.

`\begin{aligned} \epsilon_(S) &= (\epsilon_(P)\, N_(S))/(N_(P)) \\ &= (30.0\; {\rm V}) \, (980)/(340) \\ &\approx 86.5\; {\rm V}\end{aligned}`.