Answer
$a)$ $R=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
$b)$ $R=\dfrac{20}{3}$ $\Omega\approx6.67$ $\Omega$
Work Step by Step
$R=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$
$a)$
Evaluate the sum of fractions in the denominator:
$R=\dfrac{1}{\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}=\dfrac{1}{\dfrac{R_{1}+R_{2}}{R_{1}R_{2}}}=...$
Evaluate the division:
$...=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$
$b)$ $R_{1}=10$ $\Omega$ and $R_{2}=20$ $\Omega$
Substitute the values of $R_{1}$ and $R_{2}$ into the solution found on part $a)$ and evaluate to find the total resistance:
$R=\dfrac{(10)(20)}{10+20}=\dfrac{200}{30}=\dfrac{20}{3}$ $\Omega\approx6.67$ $\Omega$
