Chapter 18, Problem 18P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# (a) Find the current in each resistor of Figure P18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff’s laws: one with the node rule; a second using the loop rule through the battery, the 6.0-Ω resistor, and the 24.0-Ω resistor; and the third using the loop rule through the 12.0-Ω and 24.0-Ω resistors. Solve to check the answers found in part (a).Figure Pl8.18

(a)

To determine
The current in each resistor from the figure 1.

Explanation

Given Info: The resistance of the parallel combination is R12=12â€‰Î© and R24=24â€‰Î© , the resistance between the points a and b is R6=6.0â€‰Î© , The potential difference between the points a and e is 42â€‰V and resistance between the pointâ€™s a and e is 14.0â€‰Î© .

Explanation:

The following figure shows the current in each resistor.

Formula to calculate the equivalent resistance of the parallel combination between the pointâ€™s b and e resistors is,

1Rbe=1R12+1R24

• Rbe is the equivalent resistance between the pointâ€™s b and e,
• R12 and R24 is the resistors,

Thus, the equivalent resistance of the parallel combination between the points b and e is 8.0â€‰Î© .

Formula to calculate the total resistance between the pointâ€™s a and e resistors is,

Rae=Rab+Rbe

• Rae is the total resistance between the pointâ€™s a and e,
• Rab is the resistance between the pointâ€™s a and b,

Thus, the total resistance between the pointâ€™s a and e is 14.0â€‰Î© .

Formula to calculate the total current supplied by the battery is,

Itotal=Î”VaeRae

• Itotal is the total current,
• Î”Vae is the potential difference between the points a and e,

Substitute 42â€‰V for Î”Vae , and 14.0â€‰Î© for Rae .

Itotal=42â€‰V14

(b)

To determine
The current in each resistor from part (a) and check the answer.

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