Ohm's Law

Insert the resistance in ohms and the current in amperes; the product gives the voltage in volts. Example: I = 0.05 A flows through R = 220 Ω, so U = 220 × 0.05 = 11 V. If you need another quantity, rearrange: I = U/R or R = U/I. A proven aid is the URI triangle: U on top, R and I below. Cover the unknown quantity and the arrangement of the remaining two automatically shows whether to multiply or divide. Be strict about SI units: milliamperes must be divided by 1,000 before substituting, kiloohms multiplied by 1,000.

It strictly holds only for ohmic conductors whose resistance stays constant regardless of voltage and current. That applies well to metals at constant temperature. An incandescent lamp is the classic counterexample: its tungsten filament heats to over 2,000 °C in operation, the resistance rises to a multiple of the cold resistance, and the U-I curve bends. Diodes, transistors and electrolytes also do not follow the law. For such components you can still compute R = U/I at any operating point, but it is then only a pointwise value, not a constant. In exams, check first whether the conductor is assumed to be ohmic.

Divide both sides by the quantity you want to remove. Solved for the current: I = U/R; at a fixed voltage, less current flows through a larger resistance. Solved for the resistance: R = U/I, which is how a multimeter measures resistance indirectly via voltage and current. Worked example: R = 180 Ω is connected to a 9 V battery, so I = 9/180 = 0.05 A = 50 mA. Always check the result via the units: volts divided by ohms gives amperes, volts divided by amperes gives ohms. Once you have applied the formula a few times in every direction, you will no longer need the triangle.

Voltage U is the driving strength for charge carriers; it describes how much energy is available per charge (volt = joule per coulomb). Current I counts how much charge flows through the cross-section per second (ampere = coulomb per second). Resistance R describes how strongly the conductor impedes this flow. The water model helps: voltage corresponds to a height difference or pump pressure, current to the flow rate, resistance to a narrow section of pipe. Ohm law connects the three: more pressure means more flow, a narrower section less. Never confuse U (measured across a component) with I (measured through it).

Because the current does not depend on the voltage alone but on the ratio I = U/R. A very large resistance lets only little current through even at high voltage. Example: at 230 V a 46 kΩ resistor draws only I = 230/46,000 = 5 mA. Many safety considerations rest on exactly this: dry skin has a high resistance and limits the current, while moist skin lowers the resistance drastically, which is why electricity is so dangerous in wet conditions. Conversely, in a short circuit (R near zero) a huge current flows even at a small voltage and overheats cables. What matters is always the interplay of both quantities, never one alone.