Effect of Circuit Tolerances

Electricity and Magnetism Level 3

A DC voltage source is connected across a load resistor. The nominal voltage value is 1 1 volt, and the nominal resistor value is 1 Ω 1 \, \Omega .

Suppose many of these circuits are built, and that the manufacturing process is not perfect. The actual DC voltage can vary from 0.9 0.9 volts to 1.1 1.1 volts, and the actual resistor value can vary from 0.9 Ω 0.9 \, \Omega to 1.1 Ω 1.1 \, \Omega .

The probability distributions for both parameters are uniform over their respective ranges.

When the circuit is in operation, what is the expected value of the current flowing through the resistor? If the value is I I , enter your answer as ( I − 1 ) (I - 1) .

Note: To get this right, the answer must be within 3 percent of the expected value, per Brilliant's system. Therefore, be careful with rounding.


The answer is 0.003353477.

Steven Chase by Steven Chase , 37, USA

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1 solution

Steven Chase
Nov 5, 2019

Take a weighted sum over the parameter space, as shown in the attached code. 

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import math

N = 5000

Area_ref = (1.1 - 0.9)**2.0

dR = (1.1 - 0.9)/N
dV = (1.1 - 0.9)/N

######################################

Isum = 0.0

V = 0.9

while V <= 1.1:

    R = 0.9

    while R <= 1.1:

        I = V/R

        Isum = Isum + I*dR*dV

        R = R + dR

    V = V + dV

######################################

Isum = Isum / Area_ref

print N
print Isum
print (Isum-1.0)

#5000
#1.00335361213
#0.0033536121296

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