ขอต้อนรับ ผู้มาเยือน กรุณา ล็อกอิน หรือ สมัครสมาชิก

ล็อกอินด้วยชื่อผู้ใช้ รหัสผ่่าน และระยะเวลาใช้งาน

 
Advanced search

41330 Posts in 6202 Topics- by 8771 Members - Latest Member: ChinNaaek
Pages: 1   Go Down
Print
Author Topic: GR8677.064  (Read 2606 times)
0 Members and 1 Guest are viewing this topic.
conantee
SuperHelper
*****
Offline Offline

Posts: 1400

เราเป็นอย่างไร สังคมเป็นอย่างนั้น


« on: January 06, 2010, 11:54:56 AM »

64. An alternating current electrical generator has a fixed internal impedance R_g + jX_g and is used to supply power to a passive load that has an impedance R_g + j X_l, where j = \sqrt{-1}, R_g \neq 0, and X_g \neq 0. For maximum power transfer between the generator and the load, X_l should be equal to
(A) 0
(B) X_g
(C) -X_g
(D) R_g
(E) -R_g
« Last Edit: October 11, 2010, 11:26:35 AM by conantee » Logged
conantee
SuperHelper
*****
Offline Offline

Posts: 1400

เราเป็นอย่างไร สังคมเป็นอย่างนั้น


« Reply #1 on: October 11, 2010, 11:51:03 AM »

Don't be scared by complex numbers. Just do everything as if they are real numbers. Then, when we want to extract the information from the calculation, just consider real part.
Suppose the voltage from generator is \tilde{V}. This voltage goes across internal impedance (let's call in Z_1) and passive load (Z_2) in series.

The current in the circuit is now just \tilde{I} = \frac{\tilde{V}}{Z_{tot}} = \frac{\tilde{V}}{Z_1+Z_2}

Power to the load is just \tilde{P} = \tilde{I}^2 Z_2 = \tilde{V} \frac{Z_2}{(Z_1+Z_2)^2}

Now, Z_1 + Z_2 = (R_g + jX_g) + (R_g + jX_l) = 2R_g + j(X_g + X_l). To avoid large amount of calculation, let's use hand-waving argument. In order to keep the norm of the denominator small (so that the power is large), the imaginary part should go to zero. Otherwise, it will introduce some phase and larger denominator. This sounds like cheating since we haven't taken account of Z_2 at numerator. However, the denominator has power of two, while the numerator has only one. So, it's OK.

Hence, to make imaginary part of Z_1 + Z_2 be zero, X_l = - X_g

The correct answer is (C). Only 22 of 100 people answer correctly.
Logged
Pages: 1   Go Up
Print
Jump to: