Consider the ideal transformer, where i1(t)=20cos(120πt) Amps and v1(t)=100cos(120πt−45∘) volts, and a = 1 and b = 10.
What is the rms value of i2 in amps?
what is the amplitude of i2 in amps?
What is a and b?
amplitude is 2
To find the rms value and amplitude of i2, we need to use the turns ratio of the ideal transformer. In this case, the turns ratio is given as a = 1 and b = 10.
The formula to relate the currents on the primary and secondary sides of an ideal transformer is:
I1 / a = I2 / b
Here, I1 is the current on the primary side, I2 is the current on the secondary side, a is the number of turns on the primary side, and b is the number of turns on the secondary side.
Given that i1(t) = 20cos(120πt) and a = 1, we can find the value of I1. Since I1 is the rms value, we can use the formula:
Irms = (1 / √2) * A
Where Irms is the rms value and A is the amplitude of the waveform.
So, the rms value of I1 is:
I1rms = (1 / √2) * 20 = 20/√2 ≈ 14.142 amps
Similarly, for v1(t) = 100cos(120πt−45∘) and b = 10, we can calculate the V1rms as:
V1rms = (1 / √2) * 100 = 100/√2 ≈ 70.71 volts
Now, using the turns ratio, we can calculate the rms value of I2:
I2rms = (I1rms / a) * b = (14.142 / 1) * 10 = 141.42 amps
Therefore, the rms value of i2 is approximately 141.42 amps.
To find the amplitude of i2, we can use the formula:
A2 = (√2) * I2rms = (√2) * 141.42 = 200 amps
Therefore, the amplitude of i2 is 200 amps.