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Chapter 21: Q37PE (page 776)

Apply the loop rule to loop akledcba in Figure 21.52.

Short Answer

Expert verified

The loop rule to loop abcdefghija is:

25.1ΩI1-40.5ΩI2=-24V

Step by step solution

01

Definition of Kirchhoff's law

Kirchhoff's first law defines currents at circuit junctions. It states that the sum of currents flowing into and out of a junction in an electrical circuit equals the sum of currents flowing out of the junction.

02

Given information

R1=5.0Ω,E1=24V,r1=0.10ΩR2=40Ω,E2=48V,r2=0.50ΩR5=20Ω

03

Explanation for the loop akledcba

We go around the loop counter-clockwise, which is the same direction as the current I2but opposite the direction of I1In the direction of decreasing potential, we go through the emf E1.

Therefore, we have

E2-I2r2-I2R2+I1R5+I1r2-E2+I1R1=0E2-E1-I1r1+R1+R5-I2r2+R2=025.1ΩI1-40.5ΩI2=-24V

Hence, only one loop of the entire circuit is subjected to loop analysis, giving the following expression:

25.1ΩI1-40.5ΩI2=-24V

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