/sci/ - Science & Math

>>12325296
I1 is the current through the top branch, I2 is the current through the second branch, by Kirchoff's current law, the total current I = I1 + I2. By Kirchoff's voltage law, the voltage across the top resistor is the same as the voltage across the second resistor (walk around the loop to sum voltages to zero).

So, V = I1 R1, V = I2 R2. Therefore I = V/R1 + V/R2, so I/V = 1/R1 + 1/R2, since I/V = 1/Rp (total resistance), then 1/Rp = 1/R1 + 1/R2.