Answer:
The resistance must be 6.67[tex]\Omega[/tex]
Solution:
Resistance, [tex]R_{1} = 20\Omega[/tex]
Resistance, [tex]R_{2} = 10\Omega[/tex]
For the current to be the same when the switch is open or closed, the resistances must be connected in parallel as current is distributed in parallel with the same voltage across the circuit:
Thus in parallel:
[tex]\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}[/tex]
[tex]\frac{1}{R_{eq}} = \frac{1}{20} + \frac{1}{10}[/tex]
[tex]R_{eq} = 6.67\ \Omega[/tex]
