Answer:
[tex]\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}[/tex]
Explanation:
Resistors are said to be in parallel when they are connected to points at the same voltage; this means that the potential difference is the same across each resistor:
[tex]V=V_1 = V_2 = ... = V_n[/tex] (2)
As a result, the current splits through the different branches, and the total current is the sum of the individual currents through each resistor:
[tex]I_{tot} = I_1 + I_2 + ... +I_n[/tex] (1)
we can rewrite (1) by using Ohm's law:
[tex]\frac{V}{R_{eq}}=\frac{V_1}{R_1}+\frac{V_2}{R_2}+...+\frac{V_n}{R_n}[/tex]
and since by eq.(2) the potential difference through each resistor is the same, the last equation becomes
[tex]\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}[/tex]
which is the expression that gives the equivalent resistance for a group of parallel resistors.
