Why the current in a loop is the same

1. Dec 21, 2015

Gbox

If for example we have in a loop a DC and 2 resistors connected in series, the current in each resistor is different $I=\frac{V}{R_i}$ but we say that the current is $I=\frac{V}{R_1+R_2}$?

That means we are looking at the average current in a loop?

2. Dec 21, 2015

BvU

Nope. The voltages over the each of the resistors is $V_i = R_i I_i$, so $I_i=\frac{V_i}{R_i}$ but the current in each resistor is the same (it has to go somewhere and it can't go anywhere else), so $I = I_i\ \ \ \forall i$

Since $V_i = R_i I_i = R_i I$, and $V = \sum V_i$ you get $V = I (\sum R_i) \Rightarrow I = {V\over \sum R_i}$

3. Dec 21, 2015

cnh1995

Voltage across each resistor will be different. The sum of the voltages will be total applied voltage V.

4. Dec 21, 2015

Staff: Mentor

apply Kirchoff's current law to the node between the two resistors. Is it possible for the currents to be different?