Question

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

• A. $120\text{V}$
• B. $220\text{V}$
• C. $30\text{V}$
• D. $90\text{V}$

Answer 1

The correct option is A $120\text{V}$

Given:

$N_p=50$, $N_s=1500$ and ${\varphi }_p={\varphi }_0+4t$

Voltage induced in the primary coil is

$E_p=\left|\begin{array}{c}\frac{d{\varphi }_p}{dt}\end{array}\right|=\left|\begin{array}{c}\frac{d}{dt}({\varphi }_0+4t)\end{array}\right|$

$\Rightarrow E_p=4\text{V}$

The voltage across the secondary coil is,

$E_s=\frac{N_s}{N_p}{E}_p$

$\Rightarrow E_s=\frac{1500}{50}\times 4=120\text{V}$

Hence, $\left(A\right)$ is the correct answer.