5.1.2. Serial Circuits¶
Simple electronic circuit with a battery and a lamp
![\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);](../../_images/tikz-a5748cff48d5bdc4f139b2463e3d9c105a282da2.png)
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).