A resistor has a resistance of 6ohm, what resistance must be connected in parallel with it to obtain a combined residence 4ohm ?
The rule for resistors in parallel is,
1/R = 1/R1 + 1/R2 + 1/R3 + ...
Where R is the equivalent resistance and R1, R2, R3, ... are the resistances connected in parallel.
So what we have is,
1/R = 1/R1 + 1/R2
where R, the equivalent resistance, is 4 Ω,
and R1 is the 6 Ω resistance and R2 is the unknown resistance combined in parallel with the 6 Ω resistance. So,
1/4 = 1/6 + 1/R2
1/R2 = 1/4 - 1/6 = 3/12 – 2/12 = 1/12
Hence R2 = 12 Ω