5.1.2. Serial Circuits¶

$\draw (0,0) to[voltage source, v=$U$] (0,4) to[short, i=$I$] (3,4) to[R=$R_1$,v=$U_1$] (3,2) to[R=$R_2$,v=$U_2$] (3,0) to[short] (0,0); \draw (5,0) to (5,0);$

Simple electronic circuit with a battery and a lamp

Consider a circuit with two resistors in series. Again it is a closed circuit and current will flow. The same current will flow through both resistors. Using Ohm’s law we then can calculate the voltages across the resistors:

$\begin{split}U_1 = I\, R_1\\ U_2 = I\, R_2\end{split}$

The total voltage across both resistors is $U_1+uU2$ and is equal to the battery voltage $U$ . So:

$U = U_1 + U_2 = I\, R_1 + I\, R_2 = I\, (R_1 + R_2)$

i.e. the two resistors in series act as one resistor with resistance $R = R_1+R_2$ .

Our analysis above can be done for an arbitrary number of resistors in a serial circuit.

In a serial circuit the current through all resistors is the same, the voltage across each resistor is dependent on its resistance (relative to all other resistors in the circuit).