Answer
Formula
Resistance for parallel circuit.
[tex]\frac{1}{R_{Total}} = \frac{1}{R_{1}} +\frac{1}{R_{2}}[/tex]
As given
A circuit contains two devices that are connected in parallel.
if the resistance of one of these devices is 12 ohms and the resistance of the other device is 4 ohms.
[tex]R_{1} = 12\ ohms[/tex]
[tex]R_{2} = 4\ ohms[/tex]
Put in the above
[tex]\frac{1}{R_{Total}} = \frac{1}{R_{1}}+\frac{1}{R_{2}}[/tex]
[tex]\frac{1}{R_{Total}} = \frac{1}{12}+\frac{1}{4}[/tex]
L.C.M of (12,4)= 12
[tex]\frac{1}{R_{Total}} = \frac{1 + 3}{12}[/tex]
[tex]\frac{1}{R_{Total}} = \frac{4}{12}[/tex]
[tex]R_{Total} = \frac{12}{4}[/tex]
[tex]R_{Total} = 3\ ohms[/tex]
Therefore the total resistance of the two devices is 3 ohms .
Option (b) is correct .
