Answered: An ideal battery produces a potential…

Foundations of Astronomy (MindTap Course List)

14th Edition

ISBN:9781337399920

Author:Michael A. Seeds, Dana Backman

Publisher:Michael A. Seeds, Dana Backman

Chapter25: Astrobiology: Life On Other Worlds

Section: Chapter Questions

Problem 4RQ: How does the DNA molecule produce a copy of itself?

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An ideal battery produces a potential difference of 17.45V and is connected to 4 resistors as shown below. R1 has a resistance of 2.44Ω, R2 has a resistance of 2.43Ω, R3 has a resistance of 3.39Ω, and R4 has a resistance of 1.98Ω. From this arrangement, What is the current through R4?

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Step 1

Resistor R2 and R3 are in parallel, so the net resistance due to them is

$\begin{array}{rcl} R_{23} & = & \frac{R_{2} R_{3}}{R_{2} + R_{3}} \\ = & \frac{(2.43 Ω) (3.39 Ω)}{(2.43 Ω) + (3.39 Ω)} \\ = & 1.415 Ω \end{array}$

Now, R1 and R4 is in series with $R_{23}$ , so the effective resistance of the circuit is

$\begin{array}{rcl} R & = & R_{1} + R_{23} + R_{4} \\ = & 2.44 Ω + 1.415 Ω + 1.98 Ω \\ = & 5.835 Ω \end{array}$

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