WattsUp

Basics

Circuits

Power & V

Complex

Lesson 01 — Basics

What is a Circuit?

A circuit is a closed loop that allows electric current to flow. It needs a power source, a conductive path, and a load to do useful work.

🔋Power SourceProvides EMF (e.g. battery)

〰️ConductorCarries current (wire)

💡LoadConverts energy (bulb, etc.)

🔄Closed LoopCurrent must have a complete path

Lesson 02 — Ohm's Law

Ohm's Law

The relationship between voltage, current, and resistance — the foundation of all circuit analysis.

V = I × R

I = V / RR = V / I

Voltage (V)

9 V

Resistance (Ω)

100 Ω

0.09
Current (A)

90
Current (mA)

0.81
Power (W)

Lesson 03 — Series

Series Circuits

In a series circuit, components are connected end-to-end in a single path. The same current flows through every component.

Same ICurrent is identical through every component

V addsV₁ + V₂ + V₃ = V_supply

R addsR_total = R₁ + R₂ + R₃

Lesson 04 — Parallel

Parallel Circuits

In a parallel circuit, components share the same two nodes. Each branch has the same voltage but can carry different currents.

Same VVoltage is identical across every branch

I addsI_total = I₁ + I₂ + I₃

1/R1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Lesson 05 — Power & Energy

Electrical Power & Energy

Power is the rate of energy transfer (watts). Energy is power sustained over time — what you actually pay for on your electricity bill (kilowatt-hours).

P = V × IVoltage × Current

P = I²RCurrent² × Resistance

E = P × tPower × Time (J or kWh)

Voltage (V)

12 V

Current (A)

1.00 A

Time (hours)

1.0 h

12.00
Power (W)

43200
Energy (J)

0.0120
Energy (kWh)

0 W2400 W max

💡LED Bulb — 10 WRuns 100 h on 1 kWh

🖥️Laptop — 65 W1 kWh lasts ~15 hours

🔌Kettle — 2000 WBoils in ~2 min, uses 0.07 kWh

📱Phone charger — 5 WFull charge ≈ 0.015 kWh

Lesson 06 — Voltage Divider

Voltage Divider

Two resistors in series split the supply voltage proportionally. Vout tapped between them scales with the ratio of R2 to the total resistance.

FormulaVout = Vin × R2 / (R1 + R2)

Input Voltage Vin

12 V

R1 — top (Ω)

1000 Ω

R2 — bottom (Ω)

1000 Ω

6.00
Vout (V)

50.0
Ratio (%)

6.00
Current (mA)

SensorsThermistors & LDRs shift Vout as temperature or light changes R2

ADC inputScale a 5V signal down to 3.3V for a microcontroller ADC pin

BiasSet a midpoint reference voltage in amplifier circuits

Lesson 07 — Electric Potential

Electric Potential

Electric potential is the electric potential energy stored per unit charge at a point. Voltage is the difference in potential between two points — it drives current to flow.

V = W / QWork per unit charge (J/C)

ΔV = Vₐ − VₙPotential difference

W = Q × VWork done moving charge Q

Charge Q (mC)

100 mC

Potential Difference ΔV

12 V

1200.000
Work W (mJ)

1.20000
Work W (J)

⚡Electric PotentialEnergy per unit charge at a point — measured in Volts (J/C)

🔋EMFElectromotive force — potential difference supplied by the source

〰️EquipotentialLines of equal potential — no work needed to move charge along them

📐Ground (0 V)Potential is always measured relative to a reference point

AnalogyLike gravitational PE — charges at higher potential have more stored energy

DirectionConventional current flows from high (+) to low (−) potential

Unit1 Volt = 1 Joule per Coulomb (J/C)

Lesson 08 — Complex Networks

Equivalent Resistance

Real circuits often combine series and parallel groups in multiple layers. The key technique is progressive reduction — always start with the innermost (most nested) series or parallel group, replace it with a single equivalent resistor, then work outward until one resistor remains.

Step 1Identify the innermost series or parallel group

Step 2Replace with R_eq using the series or parallel formula

Step 3Repeat until only one equivalent resistor remains

Lesson 08A

( R1 ∥ R2 ) + R3

A parallel pair feeds into a series resistor — the simplest mixed topology.

( R1 ∥ R2 ) — R3

R1 (Ω)

100 Ω

R2 (Ω)

100 Ω

R3 — series (Ω)

50 Ω

100
R eq (Ω)

Lesson 08B

R1 + ( R2 ∥ (R3 + R4) )

A series resistor followed by a parallel block where one branch itself contains two series resistors — 3-level reduction.

R1 — [ R2 ∥ (R3+R4) ]

R1 — series (Ω)

30 Ω

R2 — parallel top (Ω)

120 Ω

R3 — inner series (Ω)

60 Ω

R4 — inner series (Ω)

60 Ω

90
R eq (Ω)

Lesson 08C

(R1 + R2) ∥ (R3 + R4)

Two parallel branches, each containing two series resistors — reduce each branch first, then combine in parallel.

( R1+R2 ) ∥ ( R3+R4 )

R1 — branch A (Ω)

100 Ω

R2 — branch A (Ω)

100 Ω

R3 — branch B (Ω)

100 Ω

R4 — branch B (Ω)

100 Ω

100
R eq (Ω)

Circuit Lab

Simulation Lab

Configure a circuit and simulate — results come from the backend calculation engine.

Series

Parallel

Mixed

Builder

Series Circuit

Battery Voltage

9 V

R1 (Ω)

100 Ω

R2 (Ω)

200 Ω

R3 (Ω)

150 Ω

What is a Circuit?

Ohm's Law

Series Circuits

Parallel Circuits

Electrical Power & Energy

Voltage Divider

Electric Potential

Equivalent Resistance

( R1 ∥ R2 ) + R3

R1 + ( R2 ∥ (R3 + R4) )

(R1 + R2) ∥ (R3 + R4)

Simulation Lab

Series + Parallel

Build Your Circuit