What you'll learn
This topic forms the foundation of electrical circuits in CXC CSEC Physics. You'll master the mathematical relationship between voltage, current, and resistance, calculate resistance values in various circuit configurations, and interpret current-voltage graphs. Exam questions regularly test calculations, graph interpretation, and practical applications worth 8-12 marks per paper.
Key terms and definitions
Voltage (V) — the electrical potential difference between two points in a circuit, measured in volts (V); represents the energy transferred per unit charge.
Current (I) — the rate of flow of electric charge through a conductor, measured in amperes or amps (A); one ampere equals one coulomb of charge passing a point per second.
Resistance (R) — the opposition to current flow in a conductor, measured in ohms (Ω); depends on the material, length, cross-sectional area, and temperature of the conductor.
Ohmic conductor — a conductor that obeys Ohm's Law, producing a straight-line graph through the origin when current is plotted against voltage at constant temperature.
Resistivity (ρ) — a property of a material that quantifies how strongly it opposes current flow, measured in ohm-metres (Ω·m); different materials have different resistivities.
Electromotive force (e.m.f.) — the energy supplied by a cell or battery per unit charge, measured in volts (V); the terminal voltage when no current flows.
Internal resistance (r) — the resistance within a power source (cell or battery) that causes the terminal voltage to drop when current is drawn.
Power (P) — the rate of energy transfer in an electrical circuit, measured in watts (W); calculated using P = IV, P = I²R, or P = V²/R.
Core concepts
Ohm's Law: The fundamental relationship
Ohm's Law states that the current through a conductor is directly proportional to the voltage across it, provided the temperature remains constant. Mathematically:
V = IR
Where:
- V = voltage (volts)
- I = current (amperes)
- R = resistance (ohms)
This relationship can be rearranged to find any unknown quantity:
- I = V/R
- R = V/I
The law applies only to ohmic conductors at constant temperature. Examples include metal wires, fixed resistors, and most metallic conductors used in Caribbean electrical installations such as copper wiring in homes across Trinidad, Jamaica, and other territories.
Current-voltage (I-V) characteristics
CXC CSEC Physics examiners frequently test your ability to interpret and sketch I-V graphs:
Ohmic conductors:
- Produce a straight line through the origin
- Constant gradient = 1/R
- Current directly proportional to voltage
- Examples: metal wires at constant temperature, carbon resistors
Non-ohmic conductors:
- Curved graph or non-linear relationship
- Resistance changes with current/voltage
- Examples: filament bulbs, diodes, thermistors
Filament bulb:
- Graph curves upward (increasing resistance)
- As current increases, temperature rises
- Higher temperature increases resistance
- Common in older street lighting systems still used in some Caribbean communities
Diode:
- Conducts in forward bias (positive voltage)
- Very high resistance in reverse bias
- Used in solar panel installations increasingly common on Caribbean buildings
Factors affecting resistance
The resistance of a conductor depends on four main factors regularly tested in CXC exams:
1. Length (L):
- Resistance is directly proportional to length
- Doubling the length doubles the resistance
- R ∝ L
2. Cross-sectional area (A):
- Resistance is inversely proportional to area
- Doubling the area halves the resistance
- R ∝ 1/A
3. Material (resistivity ρ):
- Different materials have different resistivities
- Copper (ρ ≈ 1.7 × 10⁻⁸ Ω·m) is an excellent conductor
- Nichrome (ρ ≈ 1.1 × 10⁻⁶ Ω·m) has higher resistance, used in heating elements
- Caribbean power companies use aluminum conductors for transmission lines due to lower cost despite higher resistivity than copper
4. Temperature:
- For most metals, resistance increases with temperature
- More atomic vibrations impede electron flow
- For semiconductors (thermistors), resistance decreases with temperature
- Air conditioning systems in Caribbean homes use temperature-dependent resistors for climate control
The complete relationship:
R = ρL/A
Where ρ (rho) is the resistivity of the material.
Series and parallel circuits
Series circuits:
- Current is the same through all components: I_total = I₁ = I₂ = I₃
- Voltage divides across components: V_total = V₁ + V₂ + V₃
- Total resistance: R_total = R₁ + R₂ + R₃
- Adding resistors increases total resistance
Parallel circuits:
- Voltage is the same across all branches: V_total = V₁ = V₂ = V₃
- Current divides between branches: I_total = I₁ + I₂ + I₃
- Total resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
- Adding resistors decreases total resistance
- Household wiring in Caribbean homes uses parallel circuits so appliances operate independently
For two resistors in parallel, a useful formula is: R_total = (R₁ × R₂)/(R₁ + R₂)
Electrical power and energy
Electrical power calculations appear frequently in CXC CSEC Physics calculations:
Power formulas:
- P = IV (power equals current times voltage)
- P = I²R (derived by substituting V = IR)
- P = V²/R (derived by substituting I = V/R)
Energy transferred:
- E = Pt (energy equals power times time)
- E = IVt
- Measured in joules (J) or kilowatt-hours (kWh) on electricity bills
Example: A 220V electric shower commonly used in Caribbean homes draws 25A. The power consumed is: P = IV = 25 × 220 = 5500 W = 5.5 kW
Operating for 15 minutes (0.25 hours): E = Pt = 5.5 × 0.25 = 1.375 kWh
Internal resistance and e.m.f.
Real batteries and cells have internal resistance that reduces the voltage available to external circuits:
Terminal voltage: V = e.m.f. - Ir
Where:
- e.m.f. (ε) is the electromotive force
- I is the current drawn
- r is the internal resistance
When no current flows (open circuit), terminal voltage equals e.m.f.
When current increases, terminal voltage decreases due to voltage drop across internal resistance.
Practical example: Car batteries in Caribbean vehicles may show 12V when not connected, but voltage drops when starting the engine due to high current draw and internal resistance.
Worked examples
Example 1: Basic Ohm's Law calculation
Question: A resistor in a circuit has a voltage of 6.0 V across it and a current of 0.25 A flowing through it. Calculate: (a) the resistance of the resistor (2 marks) (b) the power dissipated in the resistor (2 marks)
Solution:
(a) Using Ohm's Law: V = IR
Rearranging: R = V/I
R = 6.0/0.25 = 24 Ω ✓ (answer with unit ✓)
(b) Power: P = IV
P = 0.25 × 6.0 = 1.5 W ✓ (answer with unit ✓)
Mark scheme notes: Always include units for full marks. Show working clearly for method marks even if final answer is incorrect.
Example 2: Series circuit calculation
Question: Three resistors of 10 Ω, 15 Ω, and 25 Ω are connected in series to a 12 V battery with negligible internal resistance.
(a) Calculate the total resistance of the circuit. (2 marks) (b) Calculate the current flowing through the circuit. (2 marks) (c) Calculate the voltage across the 25 Ω resistor. (2 marks)
Solution:
(a) For series: R_total = R₁ + R₂ + R₃
R_total = 10 + 15 + 25 = 50 Ω ✓ (correct method ✓, answer with unit ✓)
(b) Using V = IR: I = V/R
I = 12/50 = 0.24 A ✓ (substitution ✓, answer ✓)
(c) Voltage across 25 Ω resistor: V = IR
V = 0.24 × 25 = 6.0 V ✓ (correct current used ✓, calculation ✓)
Example 3: Parallel circuit with Caribbean context
Question: In a home in Kingston, Jamaica, two appliances are connected in parallel to a 110 V supply. A fan has a resistance of 220 Ω and a lamp has a resistance of 440 Ω.
(a) Calculate the total resistance of the circuit. (3 marks) (b) Calculate the total current drawn from the supply. (2 marks)
Solution:
(a) For parallel circuits: 1/R_total = 1/R₁ + 1/R₂
1/R_total = 1/220 + 1/440 ✓
1/R_total = 2/440 + 1/440 = 3/440
R_total = 440/3 = 146.7 Ω ✓ (correct method ✓, answer ✓)
Alternative method using product over sum: R_total = (220 × 440)/(220 + 440) = 96,800/660 = 146.7 Ω
(b) Using I = V/R:
I = 110/146.7 = 0.75 A ✓ (substitution ✓, answer ✓)
Common mistakes and how to avoid them
• Confusing voltage and current — Students often mix up which quantity is measured in volts and which in amperes. Remember: Voltage is potential difference (V for volts), current is charge flow (I for intensity, measured in amps). Check the units in the question to identify what's given.
• Incorrect series/parallel formulas — Many students add resistances for parallel circuits or use reciprocals for series. Remember: series is simple addition (R_total = R₁ + R₂), parallel uses reciprocals (1/R_total = 1/R₁ + 1/R₂). For parallel, total resistance is always less than the smallest individual resistor.
• Forgetting to rearrange Ohm's Law — Students memorize V = IR but fail to rearrange when finding current or resistance. Practice all three forms: V = IR, I = V/R, and R = V/I. Check what the question asks for and rearrange accordingly before substituting values.
• Omitting units — In CXC CSEC Physics, units are essential for full marks. Always write Ω for ohms, A for amperes, V for volts, and W for watts. Include units in working where appropriate, not just the final answer.
• Misreading I-V graph axes — Students plot voltage on the y-axis when current should be there, or calculate gradient incorrectly. Standard convention: current (I) on y-axis, voltage (V) on x-axis. Gradient = I/V = 1/R, so resistance = 1/gradient.
• Using wrong power formula — Three formulas exist (P = IV, P = I²R, P = V²/R) but students often pick randomly. Choose based on what information is given: if you have I and V, use P = IV; if only I and R, use P = I²R; if only V and R, use P = V²/R.
Exam technique for Ohm's Law and Electrical Resistance
• "Calculate" questions require units and working — CXC CSEC marks are allocated for method (showing the formula), substitution (inserting correct values), and answer with units. Even if your final answer is wrong, you can earn 2 out of 3 marks by showing clear working. Always write the formula first, substitute values on the next line, then calculate.
• Graph questions test multiple skills — Expect to plot points accurately (use a sharp pencil and ruler), draw best-fit lines (straight lines should use a ruler; don't force the line through every point), and calculate gradients (remember gradient = rise/run = ΔI/ΔV). Identify whether a conductor is ohmic (straight line through origin) or non-ohmic (curved or not through origin).
• "State" and "explain" are different commands — "State" requires a brief fact or definition (1 mark, one sentence). "Explain" requires reasoning with cause and effect (usually 2-3 marks, multiple sentences). For example: "State Ohm's Law" needs just V = IR or the proportionality statement. "Explain why a filament bulb is non-ohmic" needs multiple points about temperature increase causing resistance change.
• Practical circuit questions need component knowledge — Questions may show circuit diagrams with ammeters, voltmeters, and switches. Remember ammeters connect in series (to measure current through), voltmeters connect in parallel (to measure voltage across), and switches control current flow. Caribbean-context questions might reference solar panels, battery systems in areas with unreliable grid supply, or energy-efficient appliances.
Quick revision summary
Ohm's Law: V = IR relates voltage, current, and resistance for ohmic conductors at constant temperature. Ohmic conductors produce straight-line I-V graphs through the origin; non-ohmic conductors curve. Resistance depends on length (R ∝ L), cross-sectional area (R ∝ 1/A), material (resistivity ρ), and temperature. Series circuits: same current, voltages add, R_total = R₁ + R₂. Parallel circuits: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂. Power calculations use P = IV, P = I²R, or P = V²/R. Always include units and show working for maximum marks.