Derive the expression for the equivalent resistance of three resistors connected in series. How is a parallel connection different?

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Open with the idea. In series, resistors are joined end to end, so the same current I flows through each.
2 · Draw the circuit. [Circuit: battery, key, ammeter and R₁, R₂, R₃ in one loop; V₁, V₂, V₃ marked across them]
3 · Write the working.
- By Ohm's law, V₁ = IR₁, V₂ = IR₂, V₃ = IR₃.
- V = V₁ + V₂ + V₃ = I(R₁ + R₂ + R₃).
- For the equivalent resistance, V = IRs.
- So Rs = R₁ + R₂ + R₃.
4 · Compare with parallel.
- Parallel: same voltage across each; the current divides.
- 1/Rp = 1/R₁ + 1/R₂ + 1/R₃.
- Rs is more than the largest resistor; Rp is less than the smallest.
5 · Real-life link. Home appliances are in parallel, so each gets full voltage and works on its own.
6 · Close. Hence in series, the equivalent resistance is the sum of the individual resistances.

Scoring tip: Write the voltage sum (series) or the current sum (parallel) first: that one line earns the method mark.