Power Three Ways - Electronic Circuits II & III: Decision Networks and Interfaces Step by Step

This power-three-ways lesson checks that one ideal resistor gives the same 24 W answer through P = V I, P = I^2 R, and P = V^2 / R. The agreement is exact only for the stated 12 V source, 6 ohm resistor, and 2 A current in an ideal Ohm-law model. Real circuits add resistor tolerance, heating, source limits, contact resistance, meter calibration, finite precision, and measurement uncertainty.

The same resistor power can be computed by voltage-current, current-resistance, or voltage-resistance routes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start from the same checked current

The source is 12 volts and the resistor is 6 ohm, so the current is 2 amperes.

I = \frac{V}{R} = 2\ \text{A}

Three power formulas agree

The helper checks the three exact routes and gets 24 watts each time.

P = V I = I^{2} R = \frac{V^{2}}{R} = 24\ \text{W}