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Question

When resistors 1 and 2 are connected in series, the equivalent resistance is

20.0Ω20.0 \Omega

. When they are connected in parallel, the equivalent resistance is

3.75Ω3.75 \Omega

. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

Solution

Verified
Answered 2 years ago
Answered 2 years ago
Step 1
1 of 2

Given: Rs=20ΩR_{s}=20\,\,\rm \Omega, Rp=3.75ΩR_p=3.75\,\,\rm \Omega

We can write equation for parallel and for series:

Rs=R1+R2Rp=R1R2R1+R2\begin{align*} R_s&=R_1+R_2\\ R_p&=\frac{R_1R_2}{R_1+R_2}\\ \end{align*}

we get:

R12R1Rs+RpRs=0R1220R1+75=0\begin{align*} R_1^2-R_1R_s+R_pR_s&=0\\ R_1^2-20R_1+75&=0 \end{align*}

a)

R1=5Ω\boxed{R_1=5\,\,\rm \Omega}

b)

R2=15Ω\boxed{R_2=15\,\,\rm \Omega}

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