10. A 1/8 W resistor having color code of yellow/violet/red/silver is connected across a power supply. what is the maximum voltage that can be applied to the resistor and not exceed the power rating of the resistor? prove your answer ( I.e., show mathematically why your answer is valid ).Please show all the work as much as possible1. Make sure you write out the equation as necessary2. Make sure you solve (algebraic manipulation) for the quantity that is needed3. Make sure you substitute numerical values and calculate answer with units4.Please use proper mathematical expression5.thank you. **Problem Statement:**A 1/8 W resistor having a color code of yellow/violet/red/silver is connected across a power supply. What is the maximum voltage that can be applied to the resistor and not exceed the power rating of the resistor? Prove your answer (i.e., show mathematically why your answer is valid).**Solution:**To solve this problem, we first need to determine the resistance of the resistor using the color code and then use the power formula to find the maximum voltage.**1. Determining Resistance from Color Code:**- **Yellow:** 4- **Violet:** 7- **Red:** Multiplier of 100- **Silver:** Tolerance of ±10%The resistance is calculated as:\[ \text{Resistance} = (47 \times 100) \, \text{ohms} = 4700 \, \text{ohms} \]**2. Calculating Maximum Voltage Using Power Formula:**The power rating $ P $ of the resistor is 1/8 watts. The formula for power is:\[ P = \frac{V^2}{R} \]Where $ V $ is the voltage across the resistor and $ R $ is the resistance. Rearranging the formula to solve for $ V $:\[ V = \sqrt{P \times R} \]Substituting the given values:\[ V = \sqrt{\frac{1}{8} \text{W} \times 4700 \, \text{ohms}} \]\[ V = \sqrt{587.5} \]\[ V \approx 24.24 \, \text{V} \]Hence, the maximum voltage that can be applied to the resistor without exceeding its power rating is approximately 24.24 volts.

Answered: 10. A 1/8 W resistor having color code…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Concept explainers

Question

10. A 1/8 W resistor having color code of yellow/violet/red/silver is connected across a power supply. what is the maximum voltage that can be applied to the resistor and not exceed the power rating of the resistor? prove your answer ( I.e., show mathematically why your answer is valid ).

Please show all the work as much as possible

1. Make sure you write out the equation as necessary

2. Make sure you solve (algebraic manipulation) for the quantity that is needed

3. Make sure you substitute numerical values and calculate answer with units

4.Please use proper mathematical expression

5.thank you.

**Problem Statement:**

A 1/8 W resistor having a color code of yellow/violet/red/silver is connected across a power supply. What is the maximum voltage that can be applied to the resistor and not exceed the power rating of the resistor? Prove your answer (i.e., show mathematically why your answer is valid).

**Solution:**

To solve this problem, we first need to determine the resistance of the resistor using the color code and then use the power formula to find the maximum voltage.

**1. Determining Resistance from Color Code:**

- **Yellow:** 4
- **Violet:** 7
- **Red:** Multiplier of 100
- **Silver:** Tolerance of ±10%

The resistance is calculated as:

\[ \text{Resistance} = (47 \times 100) \, \text{ohms} = 4700 \, \text{ohms} \]

**2. Calculating Maximum Voltage Using Power Formula:**

The power rating $ P $ of the resistor is 1/8 watts. The formula for power is:

\[ P = \frac{V^2}{R} \]

Where $ V $ is the voltage across the resistor and $ R $ is the resistance. Rearranging the formula to solve for $ V $:

\[ V = \sqrt{P \times R} \]

Substituting the given values:

\[ V = \sqrt{\frac{1}{8} \text{W} \times 4700 \, \text{ohms}} \]

\[ V = \sqrt{587.5} \]

\[ V \approx 24.24 \, \text{V} \]

Hence, the maximum voltage that can be applied to the resistor without exceeding its power rating is approximately 24.24 volts.

Expert Solution

Step 1

The Color coding of the resistor is:

Yellow/Violet/Red/Silver

The total resistance through the color coding is calculated as,

$1^{s t} band is Yellow which represents 4 2^{nd} band is Violet which represents 7 3^{rd} band is Red which represents the multiplier of \times 100 Ω 4^{th} band is Silver which represents The tolerance of \pm 10 % The Resistance is calculated to be : R = 47 \times 100 Ω \pm 10 % R = 4700 Ω \pm 10 % R_{m a x} = 4700 + \frac{10}{100} \times 4700 Ω = 4700 + 470 Ω = 5170 Ω R_{m i n} = 4700 - \frac{10}{100} \times 4700 Ω = 4700 - 470 Ω = 4230 Ω$

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Types of Power Station and Its Characteristics

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions