The primary and secondary coils of a transformer have 100 and 2000 turns respectively. If the total

Question

The primary and secondary coils of a transformer have 100 and 2000 turns respectively. If the total magnetic flux $\phi$ linked with the primary coil varies with time as $\phi = 3t^2 + 2t$ (where $\phi$ is in Webers and $t$ is in seconds), the instantaneous output voltage across the secondary coil at $t = 2$ s is:

Professor PC Thomas Classes · Answer

1. Find Primary Voltage ($V_p$): Induced voltage is the rate of change of the total flux.
$V_p = \frac{d\phi}{dt} = 6t + 2$
At $t = 2$ s:
$V_p = 6(2) + 2 = 14 	ext{ V}$
2. Find Secondary Voltage ($V_s$):
Use the transformer turns ratio ($\frac{V_s}{V_p} = \frac{N_s}{N_p}$).
$V_s = 14 	imes \left(\frac{2000}{100}ight)$
$V_s = \mathbf{280 	ext{ V}}$