Final answer:
True. The reciprocal resistance formula is indeed derived from the fact that total current is the sum of all the branch currents.
Step-by-step explanation:
The statement 'The reciprocal resistance formula is derived from the fact that total current is the sum of all the branch currents' is true.
The reciprocal resistance formula is derived from Ohm's Law, which states that the current through a resistor is equal to the voltage across the resistor divided by the resistance of the resistor. In a circuit with multiple resistors, the total current is the sum of the currents through each resistor.
For example, if you have two resistors R1 and R2 in parallel, the total current I is given by I = I1 + I2, where I1 is the current through R1 and I2 is the current through R2.