Series and parallel circuits
Section: Electricity & Magnetism | Syllabus: Cambridge IGCSE Physics (0625)
Series Circuits
- In a series circuit, components are connected end-to-end in a single loop
- there is only one path for current to flow
- The current is the same at every point in a series circuit
The same current flows through every component in a series circuit
P.d. in Series Circuits
Extended Only
- The total p.d. across the components in a series circuit is equal to the sum of the individual p.d.s across each component:
- V_total = V_1 + V_2 + V_3
Combined e.m.f. and Resistance in Series
- When cells are connected in series:
- same direction → e.m.f.s add up
- opposite direction → e.m.f.s subtract
- Resistances in series add up:
- R_total = R_1 + R_2 + R_3 + ...
Worked Example: Cells in Series
Museli connects three 1.5 V cells in series, all facing the same direction, and wants to find the total e.m.f.
- Total e.m.f. = 1.5 + 1.5 + 1.5 = 4.5 V
Worked Example: Resistors in Series
Muchindu connects a 4 Ω resistor and a 6 Ω resistor in series, and wants to find the total resistance.
- R_total = 4 + 6 = 10 Ω
Parallel Circuits
- In a parallel circuit, components are connected across each other, forming separate branches
- The current from the source is larger than the current in each individual branch
- The combined resistance of resistors in parallel is less than the resistance of the smallest individual resistor
Current splits between branches in a parallel circuit, but the p.d. across each branch is the same
P.d. in Parallel Circuits
Extended Only
- The p.d. across an arrangement of parallel resistances is the same as the p.d. across just one branch of that arrangement
The Junction Rule
Extended Only
- The sum of the currents entering a junction is equal to the sum of the currents leaving the junction
- I_in = I_out
- this is a consequence of the conservation of charge - charge cannot build up or disappear at a junction
Current entering a junction equals current leaving it: I = I₁ + I₂
Combined Resistance in Parallel
Extended Only
- Formula:
- 1R_total = (1/R_1) + (1/R_2)
Worked Example: Resistors in Parallel
Muumbe connects a 4 Ω resistor and a 12 Ω resistor in parallel, and wants to find the combined resistance.
- Step 1: write down the equation. (1/R) = (1/4) + (1/12)
- Step 2: find a common denominator and add. (1/R) = (3/12) + (1/12) = (4/12) = (1/3)
- Step 3: take the reciprocal. R_total = 3 Ω
- Notice that 3 Ω is less than either 4 Ω or 12 Ω, as expected for resistors in parallel
Advantages of Parallel Lighting Circuits
- Each lamp receives full mains voltage, so it operates at its correct brightness
- If one lamp fails, the others keep working, since each has its own independent path
- Lamps can be switched on and off independently of each other
- Adding more lamps doesn't reduce the brightness of the existing lamps
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