the primary coil of a transformer has N1 = 375 turns, and its secondary coil has N2 = 1,875 turns. If the input voltage across the primary coil is Δv = (120 V)sin ωt, what rms voltage is developed across the secondary coil?
well, the output amplitude will be 1875/375 = 5 times the input voltage, so just use that to work out the rms voltage.
To find the rms voltage developed across the secondary coil of the transformer, we need to use the turns ratio and the formula for voltage in a transformer.
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). In this case, the turns ratio is N2/N1 = 1875/375 = 5.
The formula for voltage in a transformer is given by:
V2/V1 = N2/N1
where V2 is the voltage across the secondary coil, V1 is the voltage across the primary coil, and N2/N1 is the turns ratio.
In this case, the input voltage across the primary coil is given as Δv = (120 V)sin ωt.
To find the rms voltage across the secondary coil, we can substitute the values into the formula:
V2/(120 V)sin ωt = 5
Rearranging the formula, we get:
V2 = (120 V)sin ωt * 5
The rms voltage can be found by taking the average value of the squared voltage over a complete cycle. In this case, for a sinusoidal waveform, the average value of the squared voltage is 0.5.
Therefore, the rms voltage across the secondary coil is:
Vrms = 0.5 * [(120 V)sin ωt * 5]^2
Simplifying the equation, we get:
Vrms = 0.5 * (120 V)^2 * (sin ωt)^2 * 5^2
Vrms = 0.5 * (120 V)^2 * (sin^2 ωt) * 25
Vrms = 0.5 * 120^2 * sin^2 ωt * 25
Vrms = 0.5 * 14400 * sin^2 ωt * 25
Vrms = 0.5 * 360000 * sin^2 ωt
Vrms = 180000 * sin^2 ωt
Therefore, the rms voltage developed across the secondary coil is 180000 * sin^2 ωt.