Why the current in a loop is the same

[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?

 

[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 $V = I (\sum R_i) \Rightarrow I = {V\over \sum R_i}$

 

[cnh1995]

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

 

[Dale]

2 resistors connected in series, the current in each resistor is different

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