Finding the missing value in a resistive circuit

Ohm's law relates the voltage across an ohmic component to the current through it and its resistance: U = I × R. With resistance and temperature conditions unchanged, doubling voltage doubles current. At the same voltage, doubling resistance halves current. This does not mean every electrical device behaves like a fixed resistor.

Identify the quantity before choosing the equation

U represents voltage, measured in volts, V. Many references use V for the voltage variable too. I represents current, measured in amperes, A. R represents resistance, measured in ohms. One ohm is the resistance that passes 1 A with 1 V across it. Volts, amperes and watts describe different quantities and cannot be substituted for one another.

Use U = I × R to find voltage, I = U / R to find current, or R = U / I to find resistance. The voltage must be measured across the component being analysed, and the current must flow through that same component. A resistor in a series circuit does not necessarily have the entire supply voltage across it.

Convert units first: 1 A = 1,000 mA and 1 kilohm = 1,000 ohms. Enter 20 mA as 0.020 A and 4.7 kilohms as 4,700 ohms when using the basic units. Treating the numerical milliamp value as amperes creates a thousandfold error.

The resistance value is only half the component choice

For an ohmic resistor, dissipated power is P = U × I = I² × R = U² / R. The 12 V, 120-ohm example dissipates 12 × 0.1 = 1.2 W. A 120-ohm, 0.25 W resistor is therefore unsuitable for that operating condition. Correct resistance does not prevent overheating; power selection must account for the manufacturer's temperature and mounting requirements.

At fixed resistance, doubling voltage doubles current but increases power by a factor of four. See converting amperes to watts and converting watts to amperes for related calculations. Do not assume U × I gives real power in watts for every AC load.

Using the law to explain cable losses

Suppose a DC circuit has 0.4 ohm total outgoing-and-return resistance and carries 5 A. Its voltage drop is 5 × 0.4 = 2 V, and wiring loss is 5² × 0.4 = 10 W. With 24 V at the source terminals, about 22 V remains at the load. For a long cable, counting only one conductor misses the return path.

A loose or oxidised connection can add resistance and create concentrated heating under load. A short circuit produces a very low total path impedance; the source, conductors and protective devices determine the actual current. Physical fault current is not simply infinite. Conversely, voltage may exist across an open circuit while no sustained current flows.

Where a fixed-resistance model stops working

A diode or LED has a nonlinear current–voltage characteristic. One fixed R value cannot predict every operating point. For an LED series resistor, calculate the voltage left across the resistor first: R = (supply voltage − LED forward voltage) / target current. Use the real device's forward-voltage data and current limits.

Motor current also depends on operating conditions and the back EMF generated during rotation, rather than winding resistance alone. For PWM motor control, averaged values cannot simply be inserted without considering the waveform. Linear AC circuits containing inductance or capacitance require impedance, Z. In sinusoidal steady state, current magnitude follows I_RMS = U_RMS / |Z|; for a purely resistive load, impedance equals resistance.

Checking a calculation with measurements

Use a multimeter to measure DC voltage across the relevant component. Current measurement requires a suitable series connection or an appropriate current clamp; a meter in current mode must not be placed directly across the supply. For resistance measurement, remove power, discharge stored capacitor energy and account for parallel circuit paths. With AC measurements, waveform and instrument capability matter too.

Sources

Fluke: Ohm's law and electrical calculations | ROHM: voltage, current and resistance | OpenStax: ohmic behaviour and temperature | OpenStax: impedance in AC circuits