Ohm's Law and Power

Three quantities, one equation

By the time you reach this rung you already picture voltage as the water pressure pushing on a circuit and current as the flow rate that actually moves through it. The missing piece is what decides how much flow a given push produces. That gatekeeper is resistance, and the rule that links the three is the single most-used equation in all of electronics.

Ohm's law says it in a handful of symbols: V = I times R. Read it as 'the voltage across a resistor equals the current through it multiplied by its resistance'. Push harder (more V) and more current flows; make the path narrower (more R) and less current flows for the same push. Voltage is in volts, current in amperes, resistance in ohms.

Reading the law three ways

One equation, three faces. If you know any two of V, I, and R, you can solve for the third: V = I times R, or I = V/R, or R = V/I. In practice you often measure two of them with a multimeter and let the algebra hand you the one you cannot reach directly — resistance, especially, is usually found this way rather than read straight off a meter.

A quick example: put 5 V across a 220 ohm resistor. The current is I = V/R = 5 / 220 = 0.0227 A, about 23 mA. Turn it around: if you applied 5 V and measured 23 mA flowing, you would compute R = V/I = 5 / 0.023 ≈ 220 ohm and recover the resistor's value. Same law, just rearranged for whatever you are missing.

Power: where the energy actually goes

Knowing the current is only half the story; you also need to know how much energy the part is turning into heat every second. That rate is power, measured in watts, and for any component it is simply P = V times I — the pressure across it times the flow through it. It is the exact electrical echo of hydraulic power: a big pressure drop across a fast flow means a lot of energy being spent.

For a resistor we can fold Ohm's law straight in. Substitute V = I times R and you get P = I^2 times R; substitute I = V/R and you get P = V^2/R. All three give the same number — pick whichever uses the quantities you already have. In a resistor that power has nowhere clever to go: it all becomes heat, which is exactly what power dissipation means.

Sizing a resistor so it doesn't cook

Every resistor carries a power rating — one-eighth, one-quarter, one-half watt, and so on — which is the heat it can shed before it drifts, scorches, or fails. The math above tells you the heat; your job is to pick a part rated comfortably above it. A sane rule of thumb is to run a resistor at no more than half its rating, so a part that will dissipate 100 mW wants a 1/4 W (250 mW) rating, not a 1/8 W one straining at 80 percent.

 +5V o──[ R = 300 ohm ]──►|──┐
                          LED │   (LED drops ~2 V)
                              │
 GND o────────────────────────┘

 V across R = 5 - 2     = 3 V
 I          = 3 / 300   = 0.01 A = 10 mA
 P in R     = I^2 x R   = 0.01^2 x 300 = 0.03 W = 30 mW

1. Find the voltage across the resistor. If a 5 V supply feeds a red LED that drops about 2 V, the resistor must take the remaining 5 - 2 = 3 V.
2. Choose the current you want. An LED is happy at roughly 5 to 20 mA; pick 10 mA (0.01 A).
3. Solve Ohm's law for the current-limiting resistor: R = V/I = 3 / 0.01 = 300 ohm. Round up to the nearest stock value, 330 ohm, which simply gives a touch less current.
4. Check the heat: P = I^2 times R = 0.01^2 times 300 = 0.03 W, just 30 mW.
5. Pick a part rated well above that. A common 1/4 W resistor loafs at about 12 percent of its rating — plenty of margin.

Ohm's law is a model, not a cosmic decree

Here is the honest caveat: V = I times R only holds for ohmic parts — things, like a plain resistor, whose current-versus-voltage graph is a straight line. Plenty of components are not ohmic. An LED or any diode has an exponential, sharply bending I-V curve, which is exactly why we never connect one straight across a supply and instead let a series resistor set its current. An incandescent bulb's resistance even climbs as its filament heats, so its 'R' is not constant at all.

Even a real resistor is only approximately its label. A '300 ohm' part with 5 percent tolerance is anywhere from 285 to 315 ohm, and it drifts slightly with temperature. And no real source pushes with a perfectly stiff voltage: every supply has some source resistance of its own, so drawing more current sags the voltage a little. That loading effect — and how to reason about it when you wire one stage into the next — is the thread the rest of this rung picks up.