Series Resistors

By now we have beaten to death our simple battery resistor circuit. Let us try something a little more challenging—let us put in two resistors as shown in Figure (1). In that figure we have drawn the circuit and labeled the direction of the current, and drawn in the arrows representing the voltage rises. Setting the sum of the voltage rises equal to zero
 gives

...........(1)

..........(2)

The two resistors in Figure (1) are said to be connected in series.

..........(i)

Comparing Equation (i) for a single resistor and Equation (2) for the series resistors, we see that if

.......(3)

then we get the same current i in both cases (if we use the same battery). We say that if R₁ + R₂ = R then the series resistors are equivalent to the single resistor R.

Figure 1: Two resistors in series.