Resistors in Series

For the case of capacitors we had found very interesting laws for a combination of two capacitors in series and in parallel. Now we can ask similar questions for the combination of resistors in series and in parallel.

What if we put more than one resistor into our circuit? The simplest way to do this is to put two resistors in series, as shown on the right. When two resistances are in series, the same current flows through both of them. An example of this arrangement would be a string of Christmas tree lights.

Just like for the capacitor circuits, we can also derive an equation for the equivalent resistance by considering voltage drops and currents.

• The voltage drop across resistor 1, V₁, and that across resistor 2, V₂, have to add up to the voltage provided by the battery: V₁ + V₂ = V

  and the current is the same flowing through both resistors:

  I₁ = I₂ = I
• If the single resistance R_s draws the same current as the combination, and has the same p.d., it is called the equivalent resistance. Using Ohm's Law I R_s = V

  so that

  I R_s = V = V₁ + V₂ = I₁R₁ + I₂R₂ = I R₁ + I R₂ = I $\cdot$ (R₁+ R₂)
• Therefore, R_s = R₁ + R₂

In general resistors in series simply add; so you can write for the equivalent resistance for n resistors in series:

R_s = R_i = R₁ + R₂ + R₃ + .... + R_n

© MultiMedia Physics 2000