Suppose, as in Figure 38.28

, a generator is supplying(time-averaged) power P_L to a purely resistive load R. The voltage at the generator is V₁(t) = ?2V₁ cos ?t.The power is carried to the load along a single conductor with inductance L and negligible resistance. V₂(t)is the voltage at the end of the conductor, where it connects to the load. This is an example of an LR circuit and can be analyzed using complex impedance as described in ?38.2.2. Show that the power delivered to the load is P_L = V²₁ cos² ?/R and that V₂(t) = ?2V₂ cos(?t ? ?) with V₂ = V₁ cos ?, where the phase difference ? between the voltages satisfies tan ? =?L/R. Combine these results to show that P_L = V₁V₂ sin ?/?L, thereby deriving eq. (38.16)

.

Transcribed Image Text:

V1 Z = iwL V2 R load generator