Chapter 2: Q54P (page 45)

In Figure 19.76 the resistance $R_{1}$ is $10 Ω$ , $R_{2}$ is $5 Ω$ , and $R_{3}$ is $20 Ω$ . If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?

Short Answer

Expert verified

$14 Ω$

Step by step solution

Given Data

$R_{1} = 10 Ω R_{2} = 5 Ω R_{3} = 20 Ω$

Concept

The equivalent resistance is the addition of the resistances, when the batteries are connected in series.

Determine the equivalent resistance

Resistors $R_{2}$ and $R_{3}$ are connected in parallel,

role="math" localid="1662186967334" $\begin{array}{rcl} \frac{1}{R} & = & \frac{1}{R_{2}} + \frac{1}{R_{3}} \\ = & \frac{1}{5} + \frac{1}{20} \\ = & 0.25 \\ R_{4} & = & 1 / 0.25 \\ = & 4 Ω \end{array}$

Resistors $R_{1}$ and $R_{4}$ are connected in series,

$\begin{matrix} R_{5} = R_{1} + R_{4} \\ = 10 + 4 \\ = 14 Ω \end{matrix}$

Hence, the equivalent resistance is $14 Ω$

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In Figure 19.76 the resistance $R_{1}$ is $10 Ω$ , $R_{2}$ is $5 Ω$ , and $R_{3}$ is $20 Ω$ . If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?

Short Answer

Step by step solution

Given Data

Concept

Determine the equivalent resistance

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In Figure 19.76 the resistance R1 is 10Ω, R2is5Ω , and R3 is 20Ω. If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?

Short Answer

Step by step solution

Given Data

Concept

Determine the equivalent resistance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Famous Physicists

Oscillations

Geometrical and Physical Optics

Modern Physics

Fluids

Study anywhere. Anytime. Across all devices.

In Figure 19.76 the resistance $R_{1}$ is $10 Ω$ , $R_{2}$ is $5 Ω$ , and $R_{3}$ is $20 Ω$ . If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?