Suppose that two identical resistors are placed in parallel with a 12-Volt battery. The overall current in the circuit is 6 amps. Find the resistance of each register??

Hi vinita ,

The total or equivalent resistance of these two parallel resistors is simply the ratio of the battery voltage to the overall current.

That is, R_Tot = (V_Tot) / (I_Tot) = (12 Volts) / (6 Amps) = 2 Ohms.

For resistors in parallel, the overall or total resistance is expressed by the equation

                1/R_Tot = 1/_R1 + 1/_R2

Substituting 4 Ohms for each of the individual resistances leads to the overall resistance of 2 Ohms. 

Since, the potential difference is 12 V and the current in the circuit is 6 Amp, therefore by applying Ohms law the total combined resistance of the two resistors is 2 ohms. Since there are two identical resistors in parallel each resistance is say R
 Then, 1/R + 1/R =1/2.
 2/R = 1/2
Hence, R = 2 ohms.