Electric Circuits
An electric circuit is a complete path through which electric current can flow. They are the backbone of all modern technology — from home lighting to your phone charger to car electrical systems.
This guide covers Ohm's law, series and parallel circuits, combination circuits, power and energy, Kirchhoff's laws, key formulas, memory aids, and a 10-question practice quiz.
Interactive: Ohm's Law
Adjust voltage and resistance to see how current changes. V = IR
V = I × R → 12 = 1.20 × 10
Ohm's Law Triangle
Circuit Diagram
1What Are Electric Circuits and Why Do They Matter?
An electric circuit is essentially a complete path through which electric current can flow. Think of it like a closed-loop highway for electricity — for current to flow, the path must be continuous, starting from an energy source (like a battery), going through components, and returning to the source.
- Home wiring — every light, appliance, and outlet is part of a complex circuit
- Phone chargers — internal circuits convert wall electricity to charge your battery
- Car electrical systems — headlights, engine starter, dashboard all run on circuits
2What Are the Key Terms You Need to Know?
Understanding the language of circuits is crucial. Here are the essential terms you'll encounter.
Electric Current (I)
Flow of electric charge; measured in Amperes (A)
Voltage (V)
The "push" that drives current; measured in Volts (V)
Resistance (R)
Opposition to current flow; measured in Ohms (ohm)
Conductor
Material that allows current to flow easily (copper, silver)
Insulator
Material that resists current flow (rubber, plastic, glass)
EMF (Electromotive Force)
Total energy per unit charge supplied by a source (V)
Internal Resistance
Resistance within the battery itself
Power (P)
Rate of energy conversion; measured in Watts (W)
Ammeter
Measures current; connected in series
Voltmeter
Measures voltage; connected in parallel
Short Circuit
Unintended low-resistance path causing dangerously high current
Open Circuit
A break in the circuit that prevents current from flowing
3How Does Ohm's Law Work?
Ohm's Law is the cornerstone of electric circuits. It describes the relationship between voltage, current, and resistance.
V = IR
V = Voltage (Volts) — the electrical "push"
I = Current (Amperes) — the flow of charge
R = Resistance (Ohms) — the opposition to flow
What Happens When You Change V, I, or R?
Ohmic vs. Non-Ohmic Conductors
Ohmic Conductors
Obey Ohm's Law — constant resistance. V-I graph is a straight line through the origin. (Most metals at constant temperature)
Non-Ohmic Conductors
Do NOT obey Ohm's Law — resistance changes. V-I graph is curved. (Diodes, light bulbs)
4How Do Series Circuits Work?
In a series circuit, components are connected end-to-end, forming a single, continuous path for the current — like a single road with several checkpoints. Everyone must pass through every checkpoint.
Series Circuit
Current is the same through all components: Itotal = I1 = I2 = I3
Voltages add up: Vtotal = V1 + V2 + V3
Resistances add: Rtotal = R1 + R2 + R3
If one component fails, the entire circuit breaks (open circuit)
5How Do Parallel Circuits Work?
In a parallel circuit, components are connected across the same two points, creating multiple independent paths for current — like a highway splitting into several lanes, all leading to the same destination.
Parallel Circuit
Voltage is the same across all branches: Vtotal = V1 = V2 = V3
Currents add up: Itotal = I1 + I2 + I3
Reciprocal resistances add: 1/Rtotal = 1/R1 + 1/R2 + 1/R3. Total resistance is always less than the smallest individual resistance.
If one branch fails, the others continue to function
Homes are wired in parallel so each appliance gets the full voltage, can be turned on/off independently, and one device failing doesn't shut down everything else.
6How Do You Solve Combination Circuits?
Combination circuits contain both series and parallel connections. The key is to simplify step by step.
Circuit Layout
Battery
12 V
R1 (series)
4 Ω
PARALLEL GROUP
R2
6 Ω
R3
3 Ω
Rp = 2 Ω
Rtotal = R1 + Rp = 4 + 2 = 6 Ω → I = 12/6 = 2 A
Worked Example
A 12 V battery is connected to R1 (4 Ω) in series with R2 (6 Ω) and R3 (3 Ω) in parallel.
Step 1: Find parallel combination: 1/Rp = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 → Rp = 2 Ω
Step 2: Total resistance: Rtotal = R1 + Rp = 4 + 2 = 6 Ω
Step 3: Total current: I = V/R = 12/6 = 2 A
Step 4: Voltage across R1: V1 = IR1 = 2 × 4 = 8 V
Step 5: Voltage across parallel section: Vp = 12 − 8 = 4 V
Step 6: Branch currents: I2 = 4/6 ≈ 0.67 A, I3 = 4/3 ≈ 1.33 A
Check: I2 + I3 = 0.67 + 1.33 = 2.0 A = Itotal
7Power and Energy in Circuits
Electrical power is the rate at which electrical energy is converted into other forms (heat, light, motion).
Base Formula
P = IV
Power = Current × Voltage
Using R
P = I2R
Substitute V = IR
Using V
P = V2/R
Substitute I = V/R
Energy
E = Pt
Energy = Power × Time
Power is measured in Watts (W). 1 W = 1 J/s
Electrical Energy and Kilowatt-Hours
Energy = Power × Time (E = Pt). For electricity billing, the unit used is the kilowatt-hour (kWh): 1 kWh = 1000 W for 1 hour = 3,600,000 J.
Worked Example
A 60 W light bulb is left on for 5 hours. Electricity costs $0.15 per kWh.
Energy: E = 0.06 kW × 5 h = 0.3 kWh
Cost: 0.3 kWh × $0.15/kWh = $0.045 (4.5 cents)
8What Are Kirchhoff's Laws?
While Ohm's Law handles individual components, Kirchhoff's Laws are essential for analysing more complex circuits with multiple loops and junctions.
Kirchhoff's Current Law (KCL)
Conservation of Charge
ΣIin = ΣIout
At any junction, the total current entering equals the total current leaving — like water flowing through pipes at a junction.
Kirchhoff's Voltage Law (KVL)
Conservation of Energy
ΣV = 0 (in a loop)
Around any closed loop, the total voltage gains equal the total voltage drops — like hiking up and down a mountain back to your starting point.
Key Formulas at a Glance
| Concept | Formula |
|---|---|
| Ohm's Law | V = IR |
| Series resistance | Rtotal = R1 + R2 + R3 + … |
| Parallel resistance | 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + … |
| Two resistors parallel | Rtotal = (R1 × R2) / (R1 + R2) |
| Power | P = IV = I2R = V2/R |
| Energy | E = Pt |
| Kilowatt-hour | 1 kWh = 3.6 × 106 J |
| Kirchhoff's Current Law | ΣIin = ΣIout |
| Kirchhoff's Voltage Law | ΣV (around a loop) = 0 |
9Memory Aids
Draw V at the top, I and R at the bottom. Cover the variable you want: Cover V → V = IR. Cover I → I = V/R. Cover R → R = V/I.
Series = Same current, Voltage divides. Parallel = Same voltage, Current divides.
Series = longer path, more obstacles = more resistance. Parallel = more paths = less resistance (easier for current to flow).
"A" for Along (ammeter in series). "V" for Versus/across (voltmeter in parallel).
Start with P = IV. Substitute V = IR to get P = I2R. Substitute I = V/R to get P = V2/R.
10Common Mistakes Students Make
"Confusing series and parallel rules."
Always identify the type of connection first before applying current, voltage, or resistance rules. This is the most common error.
"Forgetting to take the reciprocal for parallel resistance."
A very frequent error: computing 1/Rtotal and then writing it as Rtotal without taking the reciprocal at the end.
"Not converting units before calculations."
Always convert mA to A, minutes/hours to seconds, kW to W, etc. before plugging values into formulas.
"Misplacing ammeters and voltmeters."
Ammeters go in series. Voltmeters go in parallel. Swapping them gives incorrect readings and can damage the meters.
"Ignoring internal resistance of the battery."
When the problem gives internal resistance, include it in your total resistance calculation — it's in series with the external circuit.
"Mixing up conventional current and electron flow."
Stick to conventional current (positive to negative) unless the problem specifically asks about electron flow (negative to positive).
"Simplifying combination circuits incorrectly."
Take it one step at a time. Identify the innermost series/parallel group, simplify it, redraw, and repeat. Don't try to simplify everything at once.
"Not checking if your answer is reasonable."
If you calculate 1000 A for a flashlight circuit, something went wrong! Always do a sanity check on your final answer.
Frequently Asked Questions
- What is the difference between series and parallel circuits?
- In a series circuit, components are connected end-to-end in a single path — the same current flows through all of them and voltages add up. In a parallel circuit, components are connected across the same two points — the same voltage is across all branches and currents add up.
- Why are homes wired in parallel rather than in series?
- Parallel wiring ensures each appliance receives the full supply voltage (e.g. 120 V or 240 V) and can operate independently. If one device fails, the others continue working. In a series circuit, all devices would share the voltage and if one fails, everything stops.
- What is the difference between conventional current and electron flow?
- Conventional current is the historical definition — positive charges moving from the positive terminal to the negative terminal. Electron flow is the actual direction electrons move — from negative to positive. In most high school physics, we use conventional current.
- How does an ammeter differ from a voltmeter in how it is connected?
- An ammeter measures current and must be connected in series (in the path of the current). A voltmeter measures voltage (potential difference) and must be connected in parallel (across the component). Connecting them incorrectly can give wrong readings or damage the instruments.
- What is a short circuit and why is it dangerous?
- A short circuit is an unintended, low-resistance path for current to flow, bypassing the intended load. This causes very high currents to flow, which can lead to overheating, melting wires, and fires. Circuit breakers and fuses are safety devices that protect against short circuits.
Practice Quiz
Test your understanding of electric circuits — select the correct answer for each question.
1.Which of the following describes a material that allows electric current to flow easily?
2.If the voltage across a resistor is doubled, and its resistance remains constant, what happens to the current?
3.In a series circuit with three resistors (R1, R2, R3), which statement is true?
4.Three resistors (2 ohm, 3 ohm, 5 ohm) are connected in series. What is their total equivalent resistance?
5.Three resistors (2 ohm, 3 ohm, 6 ohm) are connected in parallel. What is their total equivalent resistance?
6.A 100 W light bulb is connected to a 120 V power source. What is the current flowing through the bulb?
7.Which instrument is connected in parallel to measure the potential difference across a component?
8.According to Kirchhoff's Current Law, if 5 A of current enters a junction and 2 A leaves through one path, how much current must leave through another path?
9.Why are household appliances typically wired in parallel?
10.A 1500 W electric heater runs for 2 hours. If electricity costs $0.10 per kWh, what is the cost of running the heater?
Final Study Advice
- 1. Draw the circuit diagram for every problem — label all known values before starting calculations.
- 2. Master the VIR triangle — it's your go-to tool for quick Ohm's Law calculations.
- 3. Practice simplifying combination circuits step-by-step: identify groups, simplify, redraw, repeat.
- 4. Always check your units and verify your answer makes physical sense.
- 5. Remember: series = same current; parallel = same voltage. Get this right and everything else follows.