Circuits – Series and Parallel
Understanding how components are connected and how current and voltage behave
Circuit Design
Series and parallel connections
In a series circuit, components are connected one after another in a single loop. There is only one path for current to flow.
- Current: The same everywhere in the circuit
- Voltage: Shared between components (adds up to supply voltage)
- Resistance: Rtotal = R₁ + R₂ + R₃...
If one component fails or is removed, the circuit breaks and no current flows.
In a parallel circuit, components are connected in separate branches. Current has multiple paths to flow through.
- Voltage: The same across all branches
- Current: Splits between branches (adds up to total current)
- Resistance: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃...
Household circuits use parallel wiring so each appliance gets full voltage and works independently.
Ammeter
- • Measures current (Amperes)
- • Connected in SERIES
- • Has very LOW resistance
- • Must not break the circuit
Voltmeter
- • Measures voltage (Volts)
- • Connected in PARALLEL
- • Has very HIGH resistance
- • Placed across components
Total Resistance
60.00 Ω
R = R₁ + R₂ + R₃
Total Current
0.200 A
R₁ = 10Ω
V: 2.00V
I: 0.200A
R₂ = 20Ω
V: 4.00V
I: 0.200A
R₃ = 30Ω
V: 6.00V
I: 0.200A
Series Circuit
- • Current is SAME everywhere
- • Voltage is SHARED between components
- • Rtotal = R₁ + R₂ + R₃
- • If one fails, circuit breaks
Parallel Circuit
- • Voltage is SAME across branches
- • Current is SHARED between branches
- • 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃
- • If one fails, others still work
Series Circuit
Question:
A 12V battery is connected to three resistors in series: 4Ω, 6Ω, and 2Ω. Calculate the total resistance, current, and voltage across each resistor.
Answer:
Total resistance:
Rtotal = 4 + 6 + 2 = 12 Ω
Current (same everywhere):
I = V/R = 12/12 = 1 A
Voltage across each resistor (V = IR):
V₁ = 1 × 4 = 4 V
V₂ = 1 × 6 = 6 V
V₃ = 1 × 2 = 2 V
(Check: 4 + 6 + 2 = 12 V ✓)
In a series circuit, what happens to the current?