The rms voltage across the secondary coil of a transformer with 500 turns in the primary and 250 turns in the secondary, when supplied with 200 V (rms) in the primary, is 100 V.
The student is asking about the rms voltage developed across the secondary coil of a transformer when the primary coil is supplied with an input voltage v(t) = (200 V) cos (2πft). The transformer has 500 turns in the primary and 250 turns in the secondary. The ratio of the transformer's output to input voltage is the same as the ratio of turns in the secondary to the primary. Therefore, if the input voltage is 200 V (rms, which is implied from the cosine function form), the output voltage will be half of this because the transformer halves the number of turns (250 turns in the secondary compared to 500 turns in the primary).
To find the rms voltage of the secondary, we simply use the voltage transformation ratio:
Vs (rms) = Vp (rms) × (Ns / Np)
Where:
- Vs (rms) is the rms voltage across the secondary,
- Vp (rms) is the rms voltage across the primary (which is 200 V in this case),
- Ns is the number of turns in the secondary (250 turns),
- Np is the number of turns in the primary (500 turns).
Thus:Vs (rms) = 200 V × (250 / 500) = 100 V
Therefore, the rms voltage across the secondary is 100 V.