Series and parallel circuits
Section: Electricity & Magnetism | Syllabus: Cambridge AS Level Physics 9702
Series Circuits In a series circuit , components are connected end-to-end in a single loop. FIG 4.3.3: Series circuit Circuit showing battery connected to three lamps (L1, L2, L3) in a single loop. One ammeter (A) in the circuit shows that the same current flows through all components.
Voltmeter readings shown across each lamp add up to the battery e.m.f. Key Rules for Series Circuits Current is the same at every point in the circuit P.d.s add up to equal the total e.m.f.: V_total = V_1 + V_2 + V_3 Resistances add up: R_total = R_1 + R_2 + R_3 Combined E.M.F.
in Series When cells are connected in series: Same direction: E.m.f.s add up Opposite direction: E.m.f.s subtract Example: Cells in Series Question: Three 1.5 V cells are connected in series (same direction).
What is the total e.m.f.? Answer Total e.m.f. = 1.5 + 1.5 + 1.5 = 4.5 V Combined Resistance in Series R_total = R_1 + R_2 + R_3 + ... Example: Resistors in Series Question: A 4 Ω and a 6 Ω resistor are connected in series.
What is the total resistance? Answer R_total = 4 + 6 = 10 Ω Parallel Circuits In a parallel circuit , components are connected across each other, forming branches. FIG 4.3.6: Parallel circuit Circuit showing battery connected to three lamps in parallel (each lamp has its own branch).
Current from battery splits at junction, flows through each lamp, and rejoins. The p.d. across each lamp equals the battery e.m.f. Key Rules for Parallel Circuits P.d. is the same across each branch Current from source is larger than current in each branch Currents add up at junctions: I_total = I_1 + I_2 + I_3 Combined resistance is less than the smallest individual resistance Junction Rule The sum of currents entering a junction equals the sum of currents leaving the junction.
I_in = I_out This is a consequence of conservation of charge. FIG 4.3.8: Current at a junction A junction point where one wire carrying current I splits into two branches carrying I₁ and I₂. Equation shown: I = I₁ + I₂.
Arrows indicate current direction. Combined Resistance in Parallel 1/R_total = 1/R_1 + 1/R_2 Example: Resistors in Parallel Question: A 4 Ω and a 12 Ω resistor are connected in parallel. What is the combined resistance?
Answer 1/R = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 R_total = 3 Ω Note: 3 Ω is less than either 4 Ω or 12 Ω. Advantages of Parallel Lighting Circuits Each lamp receives full mains voltage (operates at correct brightness) If one lamp fails, others continue working (each has independent path) Lamps can be switched on/off independently Adding more lamps doesn't reduce brightness of existing lamps
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