A transformer has N1=709turns in the primary coil and N2=1848turns in the secondary coil. If the input voltage is v(t)=218cos(Ωt) V, what rms voltage, in volts, is developed across the secondary coil?
To find the RMS (Root Mean Square) voltage developed across the secondary coil of a transformer, we can use the turns ratio equation. The turns ratio is defined as the ratio of the number of turns in the secondary coil (N2) to the number of turns in the primary coil (N1).
Turns ratio (k) = N2 / N1
In this case, the turns ratio (k) can be calculated as:
k = 1848 turns / 709 turns ≈ 2.605
Now, we know that the primary coil of the transformer is connected to an input voltage of v(t) = 218cos(Ωt) V. To find the rms voltage across the secondary coil, we need to find the rms voltage across the primary coil (V1).
RMS voltage (V1) = (1 / √2) * Vmax
where Vmax is the maximum value of the sinusoidal voltage.
In this case, Vmax = 218 V. Substituting this value into the formula, we get:
V1 = (1 / √2) * 218 V ≈ 154.35 V
Now, we can calculate the rms voltage across the secondary coil (V2) using the turns ratio:
V2 = k * V1
Substituting the values, we get:
V2 = 2.605 * 154.35 V ≈ 402.61 V
Therefore, the rms voltage developed across the secondary coil of the transformer is approximately 402.61 volts.