# Finding Current and Voltage through resistors given overall voltage and resistor values

Given a setup like:

Is it possible to find current and voltage through each resistors given resistor values and overall voltage (battery voltage I suppose).

I think $$I_0=I_A=\frac{\Delta V}{R_{total}}$$

I know $I_B+I_C=I_A$ but how do I find $I_B$ if I don't have $\Delta V_B$?

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Two formulas to understand and internalize:

1) Voltage divider: For two resistors R1 and R2 in series, the voltage $V_2$ across $R_2$, relative to the total voltage $V_T$ across both resistors, is: $$\frac{V_2}{V_T}=\frac{1}{1+R_1/R_2}$$ This formula is a direct consequence of the fact that the current through the two series resistors is the same.

2) Current divider: For two resistors R1 and R2 in parallel, the current $I_2$ through $R_2$, relative to the total current $I_T$ through both resistors, is: $$\frac{I_2}{I_T}=\frac{1}{1+R_2/R_1}$$ This formula is a direct consequence of the fact that the voltage across the two parallel resistors is the same.

You can always check that you have the correct ratio by letting one resistor get very large relative to the other; for example, in the current divider, as $R_2/R_1$ goes to $\infty$, you expect the current through $R_2$ to go to 0.

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## protected by Qmechanic♦Sep 13 '13 at 8:20

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