Power Closure Audit - Electronic Circuits Step by Step

Power can be read through equivalent routes, then split into useful and wasted terms only if the total watt ledger closes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Power has three equivalent numeric routes

Once voltage, resistance, and current are tied by Ohm's law, the same watts can be read as V times I, I squared times R, or V squared divided by R.

P = V I = I^{2}R = \frac{V^{2}}{R}

Voltage and resistance rows close to exact watts

These rows keep the power calculation visible. The middle row uses 18 volts across 9 ohms, so the current is 2 amperes and the power is 36 watts.

\begin{array}{c|c|c|c}V&R&I&P\\12\ \text{V}&6\ \text{ohm}&2\ \text{A}&24\ \text{W}\\18\ \text{V}&9\ \text{ohm}&2\ \text{A}&36\ \text{W}\\24\ \text{V}&4\ \text{ohm}&6\ \text{A}&144\ \text{W}\\\end{array}

Useful and wasted watts must add back to source watts

The useful term is one quarter of the total in each row; the remaining three quarters is wasted. The split is trusted only because the two columns add back to the source power column.

\begin{array}{c|c|c}P&P_{\text{useful}}&P_{\text{waste}}\\24\ \text{W}&6\ \text{W}&18\ \text{W}\\36\ \text{W}&9\ \text{W}&27\ \text{W}\\144\ \text{W}&36\ \text{W}&108\ \text{W}\\\end{array}

The rendered row closes both route and split

For the rendered row, 18 volts and 2 amperes give 36 watts. The budget split then records 9 useful watts and 27 wasted watts.

18\ \text{V}\cdot2\ \text{A}=36\ \text{W},\quad 9\ \text{W}+27\ \text{W}=36\ \text{W}

Power closure rejects missing energy

The diagram is simple on purpose: a single loop with one measured current. The audit is the ledger. If a useful or wasted number is changed without changing the total, the helper rejects the case.

P_{\text{useful}} + P_{\text{waste}} = P_{\text{source}},\quad \frac{P_{\text{useful}}}{P_{\text{source}}}=\frac{1}{4}