The equivalent resistance of two resistors R1 and R2 is given by 𝑅𝑒𝑞 = 𝑅1 + 𝑅2 and 𝑅𝑒𝑞 =
𝑅1𝑅2
𝑅1+𝑅2
when they are connected in series and parallel respectively. If 𝑅1 = 22.0 Ω ±
5% 𝑎𝑛𝑑 𝑅2 = 47.0 ± 5% , find the maximum error in the calculation of their equivalent
resistance when they are connected in series and parallel.
"R_s=R_1+R_2"
Now errors
∆Rs =(∆R1+∆R2 )
"\u2206R_s=\\pm({0.05}+{0.05})=\\pm0.10"
"R'_s=R_1+R_2=22+48=70\\Omega"
Now
"R_{eq}=70\\pm0.10"
"\\frac{1}{R_{eq}}=\\frac{1}{R_1}+\\frac{1}{R_2}"
"\\frac{\u2206R_{eq}}{R_{eq}}=\\frac{\u2206R_1}{R_1}+\\frac{\u2206R_2}{R_2}"
"\\frac{\u2206R_{eq}}{R_{eq}}=\\pm(\\frac{0.05}{22}+\\frac{0.05}{47})"
"R_{eq}=\\frac{R_1R_2}{R_1+R_2}"
"R_{eq}=\\frac{22\\times47}{22+47}=14.98\\Omega"
"R_{eq}=14.98\\pm0.04988\\Omega"
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