We have here what is known as parallel combination of resistors.
Using the relation:
[tex] \frac{1}{ r_{eff} } = \frac{1}{ r_{1} } + \frac{1}{ r_{2} } + \frac{1}{ r_{3} }.. . + \frac{1}{ r_{n} } \\ [/tex] And then we can turn take the inverse to get the effective resistance.
Where r is the magnitude of the resistance offered by each resistor.
In this case we have, (every term has an mho in the end) [tex] \frac{1}{10000} + \frac{1}{2000} + \frac{1}{1000} \\ \\ = \frac{1}{1000} ( \frac{1}{10} + \frac{1}{2} + \frac{1}{1} ) \\ \\ = \frac{1}{1000} ( \frac{31}{20}) \\ \\ = \frac{31}{20000} [/tex]
To ger effective resistance take the inverse: we get, [tex] \frac{20000}{31} \: ohm \\ = 645 .16 \: ohm[/tex]
