Current in parallel circuits

[map7s]

This is just a general question... when trying to solve for the current in each resistor in a parallel circuit, how do you go about setting it up? (I know that the equation V=IR comes in handy...)

 

[ranger]

You could use the current divider rule. That would require you to find the total current in the circuit. Whats wrong with using V=IR?

 

[map7s]

What is the current divider rule?

 

[ranger]

Its used to find current when resistances are hooked up in parallel with each other. Here is a wiki picture that should clear things up for you:
http://upload.wikimedia.org/wikipedia/en/4/47/Cdr.GIF [Broken]

 

[map7s]

That really helped! But if the circuit has three branches in parallel, does the formula change to I1=Itotal x ((R2+R3)/(R1+R2+R3)) ?

 

[ranger]

It changes a little when we have more than two resistances. Lets consider a circuit with three parallel branches. We know that the voltage drop across any resistor in a parallel circuit is equal to that of the source:

$$I_x = \frac{V_s}{R_x}$$

$$V_s = I_TR_T$$ <--the source voltage is equal to the total current times the total resistance.

Now substituting $I_TR_T$ for V_s in the first equation (I_x).

$$I_x = \frac{I_TR_T}{R_x}$$

We can therefore conclude that the current through any parallel resistor is in fact:
$$I_x = \frac{R_T}{R_x}\cdot I_T$$

Hope it helps/