Electricity Practice Problems

Get every prefix into base units first

Circuit values are quoted in the units components are sold in, and the formulas want volts, amps, ohms, farads and seconds. 50 mA is 0.05 A, 10 kΩ is 10,000 Ω, and 100 nF is 1 × 10⁻⁷ F. Do this once at the top of the working.

Then be precise about which voltage a formula wants. Ohm’s law relates the current through a component to the voltage across that component, not the supply voltage. A resistor in series with an LED gets only what is left after the forward drop.

Five ways a circuit answer goes wrong

• Milliamps treated as amps. 12 V at 50 mA is 12 / 0.05 = 240 Ω. Using 50 A returns 0.24 Ω, out by a factor of a thousand.
• The whole supply across the series resistor. A 3.2 V white LED at 20 mA from 5 V needs (5 − 3.2) / 0.02 = 90 Ω. Ignoring the forward drop gives 250 Ω and an LED at well under half its intended current.
• Nanofarads read as microfarads. 10 kΩ with 100 nF is a 1 ms time constant and a 159 Hz cutoff. The same resistor with 100 µF is 1 second and 0.159 Hz.
• One-way cable length. Current goes out on one core and back on the other, so a load 15 metres away is 30 metres of copper: 0.5034 Ω in 1 mm², dropping 5.03 V at 10 A. The one-way figure halves both.
• Resistance without dissipation. 12 V at 50 mA is 0.6 W, so the 240 Ω answer is right and a quarter-watt part there will drift and discolour. P = I²R is a second calculation, not a footnote.

Checking by exponent and by anchor

A few anchors catch most slips. 1 kΩ across 5 V passes 5 mA. A capacitor is 63 percent charged after one time constant and 99.3 percent after five, which is why five time constants is the working definition of settled.

Then check the exponents. Power and stored energy both square their voltage or current term, so a 10 percent error in voltage is 21 percent in the energy held by a capacitor. A time constant is linear in both resistance and capacitance. Wire resistance is linear in length and inverse in area, so doubling the diameter quarters it, which matters because cable is sold by diameter.

The part is not its nominal value

The arithmetic here is exact and the components are not. E12 resistors are typically ±10 percent, electrolytic capacitors commonly ±20 percent, and an LED’s forward voltage varies between parts from the same reel. A resistance of 137 Ω is correct and 150 Ω is what you can buy, which is why the calculators round up to the next E12 value: for current limiting, larger is the safe direction.

Resistivity carries its own trap. Materials tables quote it in microohm centimetres at 20 °C, and 1 µΩ·cm is 10⁻⁸ Ω·m, not 10⁻⁶: copper 1.678, aluminium 2.65, nichrome 110. Copper then rises about 0.393 percent per degree Celsius, so a conductor working at 70 °C carries roughly 20 percent more resistance than the table value suggests.