Question

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux linked with the primary coil is given by $\varphi ={\varphi }_0+4t$, where ϕ is in webers, t is time in seconds and ${\varphi }_0$ is a constant, the output voltage across the secondary coil is ____.

Answer 1

Step 1: Given parameters

Primary coil turns ( $N_p$) = $50$

Secondary coil turns ($N_s$) = $1500$

Magnetic flux = $\varphi ={\varphi }_0+4t$

Step 2: Calculation of secondary coil flux

Magnetic flux linked with the primary coil ( $E_p$) = $\frac{d\varphi }{dt}=\frac{d({\varphi }_0+4t)}{dt}=4Volts$

Induced emf in the secondary coil is given by

$\frac{E_s}{E_p}=\frac{N_s}{N_p}$

$\frac{1500}{50}=\frac{E_s}{4}$

$$\begin{gathered} E_s=\frac{1500}{50}\times 4 \\ =120V \end{gathered}$$

Induced emf in the secondary coil is $120V$.