DC Circuits Unlocked: Master Any Circuit in Trinité-et-Tobago | ORBITECH

Ohm's Law: Your First Circuit Tool

Ohm's Law states that current through a conductor equals voltage divided by resistance: I = V/R. $I = \frac{V}{R}$
Remember "VIR" triangle: V on top, I and R below
For any resistor, V = I × R tells you the voltage drop across it. $V = I \cdot R$
Higher resistance = bigger voltage drop for same current
Power dissipated in a resistor is P = V × I = I²R = V²/R. $P = V \cdot I = I^{2} \cdot R = \frac{V^{2}}{R}$
Use P = I²R when current is known, P = V²/R when voltage is known

V = I \cdot R

In series circuits, current is the same through all components: $I_{t} o t a l$ = I₁ = I₂ = ... $I_{total} = I_{1} = I_{2} = . . .$
Series circuits have only ONE path for current to flow
Total resistance in series equals sum of individual resistances: $R_{t} o t a l$ = R₁ + R₂ + ... $R_{total} = R_{1} + R_{2} + . . .$
Add resistances like stacking blocks - more resistance = harder for current
Voltage divides across series resistors proportionally to their resistance values. $V_{n} = I \cdot R_{n}$
Bigger resistor gets bigger voltage drop - think of it as sharing the 'voltage pie'

R_{total} = R_{1} + R_{2} + . . .

In parallel circuits, voltage is the same across all branches: $V_{t} o t a l$ = V₁ = V₂ = ... $V_{total} = V_{1} = V_{2} = . . .$
All parallel branches share the same voltage - like different roads to the same place
Total resistance in parallel is less than any individual resistance. $\frac{1}{R_{total}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + . . .$
More parallel paths = easier for current = lower total resistance
Current divides inversely with resistance in parallel circuits. $I_{n} = \frac{V}{R_{n}}$
Smaller resistance gets bigger current - like water flowing through wider pipes

\frac{1}{R_{total}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + . . .

Kirchhoff's Current Law (KCL): Sum of currents entering a junction equals sum leaving. $\sum I_{in} = \sum I_{out}$
What goes in must come out - like water flowing through pipes
Kirchhoff's Voltage Law (KVL): Sum of voltage drops equals sum of voltage sources in any loop. $\sum V_{drops} = \sum V_{sources}$
Voltage rises must equal voltage drops around any closed loop
Use KVL to write equations for each loop in a circuit.
Mark loop directions with arrows before writing equations

\sum V_{drops} = \sum V_{sources}

Voltage divider splits input voltage across series resistors proportionally. $V_{out} = V_{in} \cdot \frac{R_{2}}{R_{1} + R_{2}}$
Output voltage is fraction of input - adjust resistor values to get your desired voltage
Works only for series circuits with no load on the output.
If you connect a load, the output voltage changes - voltage divider becomes loaded
Common use: creating reference voltages for sensors and circuits.
Perfect for powering small circuits from a bigger supply

V_{out} = V_{in} \cdot \frac{R_{2}}{R_{1} + R_{2}}

Current divider splits total current among parallel resistors inversely. $I_{n} = I_{total} \cdot \frac{R_{total}}{R_{n}}$
Smaller resistor gets bigger share of current - like traffic lanes
Current divides inversely with resistance values.
Double one resistor's value and its current halves (approximately)
Useful for current sensing and load balancing applications.
Great when you need to measure current through specific branches

I_{n} = I_{total} \cdot \frac{R_{total}}{R_{n}}

Power rating tells you maximum safe power a resistor can dissipate. $P_{max} = I_{max}^{2} \cdot R = \frac{V_{max}^{2}}{R}$
Always check power rating - a 1/4W resistor burning 1/2W will smoke!
Total power in a circuit equals sum of power dissipated by all components. $P_{total} = \sum P_{n}$
Power in = power out - energy conservation applies to circuits too
Calculate power using P = VI = I²R = V²/R depending on what you know. $P = V \cdot I = I^{2} \cdot R = \frac{V^{2}}{R}$
Choose the formula that uses your known values to save time

P = V \cdot I = I^{2} \cdot R = \frac{V^{2}}{R}

Street lights in Port-of-Spain often use series circuits for simple control.
If one light fails, they all go out - series circuits are simple but fragile
Your phone charger uses a voltage divider to create 5V from 240V mains.
That little box converts dangerous 240V to safe 5V for your phone
House wiring in Chaguanas uses parallel circuits so appliances work independently.
Turn off the fridge, your TV still works - parallel circuits are robust
Calculate cost to run your laptop for 8 hours: P = 65W, cost = 65W × 8h × TT$0.80/kWh. $E = P \cdot t = 65 W \times 8 h = 0.52 kWh$
TT$0.80 per kWh is typical residential rate - check your bill!

E = P \cdot t

Ohm's Law discovered by Georg Ohm in 1827: Fundamental relationship between voltage, current, and resistance
Kirchhoff's Laws published by Gustav Kirchhoff in 1845: Rules for current and voltage in electrical networks
CSEC Physics exam includes 20% circuit analysis questions: Master these techniques for top marks in your exams
TT$100 can power a 100W bulb for about 10 hours: Useful for estimating energy costs in local currency