Final answer:
Calculating the rms magnitude of the voltage across the load impedance in a complex circuit with a linear transformer involves summing the resistances and reactances of the circuit elements and transformer. The total impedance is then used with Ohm's Law to determine the voltage across the load, but specific calculations require more detailed information on the transformer's turns ratio and other factors.
Step-by-step explanation:
To calculate the rms magnitude of the voltage across the load impedance in a series combination of a resistor and inductor connected to a sinusoidal voltage source through a linear transformer, several steps are involved. First, one must calculate the total impedance of the series circuit, which includes the internal impedance of the source, the impedance of the primary and secondary coils of the transformer, and the impedance of the resistor and inductor in series.
The impedance of the inductor (ZL) at a frequency (f) of 1000 rad/s is given by ZL = jωL, where L is the inductance in henrys. The impedance of the 100 mH inductor would be ZL = j(1000)(0.1) = j100 Ω. The total series impedance (ZT) is then the sum of the 300 Ω resistor (R), the impedance of the inductor (ZL), and the internal impedance of the source (ZS): ZT = R + ZL + ZS = 300 Ω + j100 Ω + (100 + j13.74) Ω.
The transformer's impedance also needs to be factored into the calculation, using the transformer's turns ratio (which is derived from the mutual inductance (M), the primary inductance (L1), and the secondary inductance (L2)). Once these impedances are properly combined and the equivalent impedance is found, one can use Ohm’s Law (V=IZ) to calculate the voltage across the load.
However, because the comprehensive calculation requires knowledge of the turns ratio and several other detailed considerations, a straightforward formula cannot be provided without additional information.