Question

Two identical resistors are connected first in series and second in parallel. The equivalent resistances of the two types of connections are, respectively, RS and RP. What is the ratio RS/RP?

Answer 1

Answer:

$\frac{R_{s} }{R_{p} } =\frac{R_{1} }{R_{2} }+\frac{R_{2} }{R_{1} } +2$

Explanation:

We have series and parallel combination of two resisters $R_{1}$ and $R_{2}$.

Series combination is

$R_{s}= R_{1}+R_{2}$ and Parallel is $R_{p} = (\frac{1}{R_{1}}+\frac{1}{R_{2}} )^-1$

Now dividing series equivalent resistance by parallel resistance gives us

$\frac{R_{s} }{R_{p} } =\frac{R_{1} }{R_{2} }+\frac{R_{2} }{R_{1} } +2$.

Note! series Combination is simply superposition of two elements (resisters in this case ) in a circuit.