FE Mechanical Electricity and Magnetism Practice Problems

The current FE Mechanical specification assigns 5-8 of the 110 exam questions to Electricity and Magnetism. Form A contains 6 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A 48 V ideal DC source feeds node A through a 6 $Ω$ series resistor, and a 12 $Ω$ resistor connects node A to the source return. A variable resistive load is then connected between node A and the return. The maximum power the load can absorb is most nearly:

(A)64 W
(B)144 W
(C)256 W
(D)576 W

Show worked solution

Answer: (A)

Matching the load to the 4 $Ω$ Thevenin resistance caps the transfer at 64 W, one quarter of $V_{t h}^{2} / R_{t h}$ .

Maximum transfer requires the load to equal the Thevenin resistance at the terminals, which is the 6 $Ω$ source branch in parallel with the 12 $Ω$ element.

R_{t h} = \frac{( 6 ) ( 12 )}{6 + 12} = 4 Ω

V_{t h} = 48 \times \frac{12}{6 + 12} = 32 V

Half the Thevenin voltage lands on a matched load, which is why the ceiling depends on the equivalent source alone and not on any particular load value.

P_{ma x} = \frac{V _{t h}^{2}}{4 R _{t h}} = \frac{( 32 ) ^{2}}{4 ( 4 )} = 64 W

FE Reference Handbook — Electricity and Magnetism: Thevenin Equivalent Circuit and Maximum Power Transfer

Why the other choices appear

(B)Using the 48 V source voltage in place of the 32 V Thevenin voltage gives $4 8^{2} / [4 (4)] = 144$ W.
(C)Omitting the matched-load factor of 4 gives $3 2^{2} /4 = 256$ W.
(D)Committing both errors together gives $4 8^{2} /4 = 576$ W.