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Question

# When resistors 1 and 2 are connected in series, the equivalent resistance is$20.0 \Omega$. When they are connected in parallel, the equivalent resistance is$3.75 \Omega$. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

Solution

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Step 1
1 of 2

Given: $R_{s}=20\,\,\rm \Omega$, $R_p=3.75\,\,\rm \Omega$

We can write equation for parallel and for series:

\begin{align*} R_s&=R_1+R_2\\ R_p&=\frac{R_1R_2}{R_1+R_2}\\ \end{align*}

we get:

\begin{align*} R_1^2-R_1R_s+R_pR_s&=0\\ R_1^2-20R_1+75&=0 \end{align*}

a)

$\boxed{R_1=5\,\,\rm \Omega}$

b)

$\boxed{R_2=15\,\,\rm \Omega}$

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