two resistors, r1 and r2, are connected in parallel. r2 = 221.0 ohms, and the equivalent resistance of the…

Explanation:

Step1: Recall parallel - resistance formula

The formula for the equivalent resistance $R_{eq}$ of two resistors $R_1$ and $R_2$ in parallel is $\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$. We want to solve for $R_1$, so we can rewrite the formula as $\frac{1}{R_1}=\frac{1}{R_{eq}}-\frac{1}{R_2}$.

Step2: Substitute the given values

Given $R_{eq} = 120.7\ \Omega$ and $R_2=221.0\ \Omega$. $\frac{1}{R_1}=\frac{1}{120.7}-\frac{1}{221.0}$. First, find a common - denominator. The common denominator of 120.7 and 221.0 is $120.7\times221.0$. $\frac{1}{R_1}=\frac{221.0 - 120.7}{120.7\times221.0}$. $\frac{1}{R_1}=\frac{100.3}{120.7\times221.0}$. $120.7\times221.0 = 120.7\times(200 + 20+1)=120.7\times200+120.7\times20 + 120.7\times1=24140+2414+120.7 = 26674.7$. So, $\frac{1}{R_1}=\frac{100.3}{26674.7}$.

Step3: Solve for $R_1$

$R_1=\frac{26674.7}{100.3}$. $R_1 = 266\ \Omega$.

Answer:

266