P3.3 - Series and Parallel circuits

Series circuit

A string of two or more components connected end-to-end in the same loop to a power supply

Parallel circuit

Two or more components attached along separate branches of the circuit

Current in a series circuit

Same at all points around the loop

PD in a series circuit

Shared between the individual components; the sum of PDs across components equals the PD of the power supply

Two disadvantages of series circuits

(1) If one component breaks, all others stop working.

(2) Components cannot be controlled (switched on/off) separately

Advantages of parallel circuits

Components can be individually controlled using their own switches; if one component stops working, others continue to function

Current in a parallel circuit

Current splits at junctions — some goes one way, rest goes the other; current in each branch is smaller than the current from the power supply

PD in a parallel circuit

Voltage across each component in parallel is the same

Summary: Series vs Parallel

Series — current: same; voltage: shared; resistance: R_total = R₁ + R₂ + R₃. Parallel — current: splits; voltage: same across each branch; resistance: R_total < smallest individual R

Combined resistance in series

R = R₁ + R₂ + R₃ + … — total resistance is the SUM of individual resistances

Why does adding resistors in series INCREASE total resistance?

More resistors means charge has more to pass through → greater overall opposition to current

Combined resistance in parallel

Total (net/combined) resistance DECREASES — always LESS than the smallest individual resistor

Why does adding resistors in parallel DECREASE total resistance?

Each resistor creates an extra path along which charge can flow → more charge can flow overall → smaller overall resistance

Total voltage in series (equation)

V_total = V₁ + V₂ + V₃ (sum of PDs across each component)

Total current in parallel (equation)

I_total = I₁ + I₂ + I₃ (sum of currents in each branch)

Worked example: finding R₂ in series

Step 1: Write equation for combined resistance (R = R₁ + R₂ + R₃).

Step 2: Substitute values.

Step 3: Rearrange for unknown (R₂ = R − R₁ − R₃)

[PAG] Aim: Investigating Series & Parallel Circuits

Use resistors and filament lamps to test series and parallel circuits; start with a single resistor/lamp in series with a cell, then build with additional resistor in series OR parallel

[PAG] Independent variable

Potential difference, V

[PAG] Dependent variable

Current, I

[PAG] Control variables

PD of power supply; use of the same equipment (wires)

[PAG] Equipment

Cell/battery, ammeter, voltmeter, fixed resistors, filament lamp, switch, connecting wires

[PAG] Method (step-by-step)

(1) Set up circuit with single fixed resistor. (2) Record voltage (voltmeter) and current (ammeter). (3) For each pair of V and I, calculate resistance and record. (4) Change resistor, repeat steps 2-3. (5) Arrange two resistors in SERIES, repeat. (6) Arrange two resistors in PARALLEL, repeat. (7) Replace fixed resistor with filament lamp, repeat from step 1

[PAG] Analysis equation

R = V ÷ I (calculate resistance for each voltage/current reading)

[PAG] Expected results: series

Total resistance of two resistors in series = SUM of their individual resistances

[PAG] Expected results: parallel

Total resistance of two resistors in parallel = LESS than either of the individual resistances

[PAG] Systematic errors

Voltmeter and ammeter should start from zero — avoid zero error

[PAG] Random errors

Voltmeter and ammeter have small resistance → readings slightly inaccurate; temperature of equipment could affect resistance (must be controlled); take multiple readings to reduce uncertainty

[PAG] Safety considerations

(1) High current through thin wire makes it very hot — don't touch when on. (2) Switch off power supply if burning smell detected. (3) No liquids near equipment. (4) Components get hot at high voltage — careful handling, especially filament lamp. (5) Disconnect between readings to avoid overheating

Current at a junction rule

Current flowing INTO a junction = current flowing OUT of junction (charge is conserved)

Direction of conventional current

From POSITIVE terminal to NEGATIVE terminal of cell/battery (through external circuit)

Direction of electron flow

From NEGATIVE terminal to POSITIVE terminal — OPPOSITE to conventional current

Why are conventional current and electron flow opposite?

Conventional current was defined as positive charge flow before electrons were discovered; actually electrons (negative) move the other way

Worked example: finding missing current at a junction

Step 1: Recall current is conserved at a junction. Step 2: Identify total current flowing IN. Step 3: Subtract the known branch current(s) from total to find the missing one

Testing resistance: components investigated

Filament lamps, diodes, thermistors, LDRs — all have variation of resistance that needs testing

Circuit for testing resistance (universal setup)

Voltmeter in PARALLEL across component being tested; ammeter in SERIES with rest of components; variable resistor in series to control current

Equation for calculating resistance in PAG

R = V ÷ I

Testing filament lamp / diode

Current (independent variable) changed using variable resistor; voltage across component measured with voltmeter; resistance calculated for each reading

Testing LDR: method

(1) Begin with lamp turned off — dark room.

(2) Record voltmeter and ammeter readings.

(3) Slowly increase light intensity using dimmer switch.

(4) Record readings at each step

Testing thermistor: method

(1) Begin with heater turned off.

(2) Record voltmeter and ammeter readings.

(3) Slowly increase temperature using dimmer switch.

(4) Record readings at each temperature

Testing LDR/thermistor: important rule

Lamp/heater must be CLOSE but NOT TOUCHING the component; wait a few seconds for LDR/thermistor to react to the environmental change before taking readings

Exam tip: circuit diagrams for testing resistance

(1) Ammeter in series. (2) Voltmeter in parallel across component. (3) Use correct circuit symbol. (4) Include variable resistor to vary current. (5) Connect to power supply (below 15 V) to avoid affecting component resistance

What is electrical power?

The rate of energy transfer, or the amount of energy transferred per second

What does power of a device depend on?

The voltage (PD) of the device; the current through the device

Unit of power

Watt (W); 1 W = 1 joule per second (1 J/s)

Power equation 1

P = I × V; where P = power (W), I = current (A), V = potential difference (V)

Power equation 2 (in terms of resistance)

P = I² × R (derived by combining P = IV with V = IR)

Power equation 3 (in terms of resistance)

P = V² ÷ R (derived by combining P = IV with I = V/R)

When to use P = I²R vs P = V²/R

P = I²R if you know current and resistance; P = V²/R if you know voltage and resistance; P = IV if you know current and voltage

Worked example: P = IV

Step 1: List known quantities. Step 2: Write equation. Step 3: Rearrange if needed. Step 4: Substitute and calculate

Mnemonic for power equations

"Twinkle Twinkle Little Star, Power equals I squared R" — helps remember P = I²R; use this when you know current and resistance

What is "work done" in a circuit?

Work is done when charge flows through a circuit; work done = energy transferred

What does energy transferred by electrical work depend on?

Current (I); potential difference (V); time (t)

Energy transferred equation 1

E = P × t; where E = energy (J), P = power (W), t = time (s)

Energy transferred equation 2

E = I × V × t (derived by substituting P = IV into E = Pt)

Energy transferred equation 3 (in terms of charge)

E = Q × V; where Q = charge (C), V = potential difference (V)

Energy conservation in a circuit

Energy supplied by battery = energy transferred to all components in the circuit (over a given time)

Worked example: E = IVt

Step 1: List known quantities (convert time to seconds). Step 2: Write equation (E = IVt). Step 3: Substitute and calculate

Exam tip: "energy transferred" vs "work done"

Used interchangeably in exam equations — mean the same thing

Exam tip: units for time in energy/power equations

Always convert time to SECONDS before using in equations (e.g. 1 minute = 60 s)