Explain why we use this formula to calculate total resistance Why do we use this formula to find the total resistance? Lets say we have three resistors in a parallel circuit
$$R_t = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$$
Where does it come from? 
 A: This is derived from the the formula for calculating total resistance in a parallel circuit
$$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
taking its inverse gives:
$$R_t = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$$
A: Think about current flow.
If we take each individual resistor and determine the current for the applied voltage, we get: $$I_T=\frac {V}{R_1} +\frac {V}{R_2} + ...$$
Dividing everything by the voltage give us: 
$$\frac {I_T}{V}=\frac {1}{R_1} +\frac {1}{R_2} + ...$$
Which is the same as:
$$\frac {1}{R_{eq}}=\frac {1}{R_1} +\frac {1}{R_2} + ...$$
We now need to invert both sides, which gives:
$${R_{eq}}=\frac {1}{\frac {1}{R_1} +\frac {1}{R_2} + ...}$$  
A: 
Why do we use this formula to find the total resistance?

Because parallel connected conductances sum just as series connected resistances.
Ohm's law is
$$V_R = RI_R $$
The dual of Ohm's law is
$$I_G = GV_G $$
Since, for parallel connected circuit elements, the voltage across is identical, it follows that, for parallel connected conductances
$$I_{total} = V\left(G_1 + G_2 + G_3 + \;... \right)$$
But 
$$G = \frac{1}{R} $$
thus
$$I_{total} = V\left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \;...\right) $$
or
$$\frac{V}{I_{total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \;...} = R_{eq}$$
