What is the equivalent resistance of two resistors of 2 ohm and 3 ohm connected in parallel?
1/R = 1/R1 + 1/R2 = (R1 + R2)/R1 R2
so
R = R1 R2 / (R1+R2)
= 6/5 = 1.2 Ohms
to derive
i1 = V/R1
I2 = V/R2
i = i1+i2 = V/R1 + V/R2
but
R = V/i = V/(V/R1 +V/R2) = 1/(1/R1+1/R2)
= R1 R2 / (R2 + R1)
To find the equivalent resistance of two resistors connected in parallel, you can use the following formula:
1/Req = 1/R1 + 1/R2 + ...
So in this case, where the resistors have values of 2 ohm and 3 ohm, the formula becomes:
1/Req = 1/2 + 1/3
Now, to find the value of Req, you need to sum the reciprocals of the resistances and then take the reciprocal of that sum:
1/Req = 1/2 + 1/3
1/Req = 3/6 + 2/6
1/Req = 5/6
To get the value of Req, take the reciprocal of 5/6:
Req = 6/5
Hence, the equivalent resistance of two resistors of 2 ohm and 3 ohm connected in parallel is 6/5 ohm.