Resistors in Series (Derivation) — Science Class 10

1. Introduction: One Path, One Current

You already know a few things from earlier in this chapter. Voltage $V$ is the push across a wire, measured in volts (V). Current $I$ is the flow through it, measured in amperes (A). And resistance $R$ , measured in ohms (Ω), is the one number for how hard a part fights that flow. Ohm's law ties them together: $V = IR$ .

Now we ask a new question. Suppose you join two or three resistors one after another, in a single line, so the current has only one road to travel. The whole chain still has some total resistance. What single resistor could you swap in to replace the whole chain and change nothing?

That single replacement is called the equivalent resistance — the one resistor that behaves exactly like the whole group put together. For resistors in series, we are going to prove, step by step, that this equivalent resistance is simply the sum:

$R_s = R_1 + R_2 + R_3$

By the end of this lesson you will not just remember that formula. You will be able to build it yourself from two simple facts, see why it has to be a sum and not anything else, and use it to find currents and voltages in a real circuit.