Ohm's Law and DC Circuits
Every circuit you build — from a simple flashlight to a phone charger — turns on the same three quantities: how hard the battery pushes (voltage), how much charge flows as a result (current), and how strongly the components in the way resist that flow (resistance). For the ohmic parts, Ohm's law, V = IR, ties them together with a proportionality simple enough to predict circuit behavior with nothing more than arithmetic, and it underlies every more advanced circuit-analysis technique that follows, from series and parallel networks to the AC circuits used in real electronics.
Voltage, current, and resistance
Current is the rate of charge flow. Resistance opposes that flow. For an ohmic resistor, doubling the voltage doubles the current.
Series and parallel combinations
Resistors in series add directly. In parallel, the reciprocal of the equivalent resistance equals the sum of reciprocals of each branch.
Ohm's Law
In a circuit, voltage is the electrical push and current is the flow of charge it produces. Ohm's law says the current through a resistor is proportional to the voltage across it — and the resistance tells you how strongly the resistor opposes that flow.
The formula
V = I · R
- V — voltage (V): the electrical push across the component
- I — current (A): the flow of electric charge through the component
- R — resistance (Ω): how strongly the component opposes the current
Worked example
A 9 V battery is connected across a 3 Ω resistor. How much current flows?
- V = 9 V
- R = 3 Ω
- I = V / R
- I = 9 V / 3 Ω
I = 3 A
Test yourself
The same 9 V battery is connected to a bigger 9 Ω resistor. What current flows now?
- 3 A
- Correct answer: 1 A
- 81 A
Correct! I = V / R = 9 V ÷ 9 Ω = 1 A — triple the resistance, a third of the current.
Where you see this
A flashlight dims steadily as its battery runs down — less voltage means less push, so less current drives the bulb, and dimmer light. A dimmer knob on a living-room light is the same law with a dial: turning it raises the resistance in the circuit, and the current — and the glow — fall accordingly.
Common mistakes
The persistent slip is treating V, I, and R as three independent settings — they are not: the battery fixes the voltage, the component fixes the resistance, and the current is the consequence, I = V / R. Swap a 3 Ω resistor for 9 Ω across the same 9 V battery and the current drops from 3 A to exactly 1 A — triple the resistance, one third the current. A second error is imagining the current gets weaker as it goes around the loop; the current is one single value set by the whole circuit.
How it connects
This is the vocabulary the entire circuits module speaks — voltage as push, current as flow, resistance as opposition — and every later rule reduces to it. Kirchhoff's laws, next, take this single-resistor relation and apply it to junctions and loops, so circuits with branches can be solved instead of just admired.