Serial Circuits
===============


   .. tikz:: 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);


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:

.. math::
   U_1 = I\, R_1\\
   U_2 = I\, R_2

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

.. math::
   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).*