(a) Approximate µP . (b) Approximate σP . (c) Write the estimate
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An engineer needs to estimate the amount of power dissipated by a wire-wound resistor. Power (in watts) can be
found by P =V2R where V is the voltage (in volts) and R is the resistance (in Ohms). In this particular application, assume the voltage V ∼ ·(µV , σ2 V = 0.22) and assume the resistance R ∼ ·(µR, σ2 R = 0.12). Assume V and R are independent. The engineer measured the voltage and resistance and found v = 14.4 volts and r = 8.2 Ohms.
(a) Approximate µP .
(b) Approximate σP .
(c) Write the estimate
![**Problem Statement:**
An engineer needs to estimate the amount of power dissipated by a wire-wound resistor. Power (in watts) can be found by:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage (in volts) and \( R \) is the resistance (in Ohms).
In this particular application, assume the voltage \( V \sim (\mu_V, \sigma_V^2 = 0.2^2) \) and assume the resistance \( R \sim (\mu_R, \sigma_R^2 = 0.1^2) \). Assume \( V \) and \( R \) are independent. The engineer measured the voltage and resistance and found \( v = 14.4 \) volts and \( r = 8.2 \) Ohms.
(a) Approximate \( \mu_P \).
(b) Approximate \( \sigma_P \).
(c) Write the estimate of the power, along with the estimated error, in engineering (i.e. \( \pm \)) notation. Be sure to state the units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F293032ce-89a7-4d5a-8a29-aae96cb1d151%2Fe4dcf8ff-88de-4996-8d83-c6ae8c44ba1e%2F4x5x6wk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
An engineer needs to estimate the amount of power dissipated by a wire-wound resistor. Power (in watts) can be found by:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage (in volts) and \( R \) is the resistance (in Ohms).
In this particular application, assume the voltage \( V \sim (\mu_V, \sigma_V^2 = 0.2^2) \) and assume the resistance \( R \sim (\mu_R, \sigma_R^2 = 0.1^2) \). Assume \( V \) and \( R \) are independent. The engineer measured the voltage and resistance and found \( v = 14.4 \) volts and \( r = 8.2 \) Ohms.
(a) Approximate \( \mu_P \).
(b) Approximate \( \sigma_P \).
(c) Write the estimate of the power, along with the estimated error, in engineering (i.e. \( \pm \)) notation. Be sure to state the units.
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