Dot convention is a source-bound sign rule in this finite model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
Dot polarity is a sign rule on cited winding voltages
The polarity row must cite two distinct winding sources before it can add or subtract them.
V out = V a ± V b V_{\text{out}}=V_a\pm V_b V out = V a ± V b Dot polarity setup The opposing row uses two checked winding sources. Np 1 Ns 1 dPhi 4 Wb dt 1 s Vp 4 V Vs 4 V mode aiding Np 1 Ns 1 dPhi 4 Wb dt 1 s Vp 4 V Vs 4 V mode aiding V1 4 V V2 4 V mode opposing Vout 0 V
Aiding adds and opposing subtracts
Equal opposing windings cancel. Equal aiding windings add. Unequal opposing windings leave the difference.
V a V b mode V out 4 V 4 V opposing 0 V 4 V 4 V aiding 8 V 6 V 4 V opposing 2 V \begin{array}{c|c|c|c}V_a&V_b&\text{mode}&V_{\text{out}}\\4\ \text{V}&4\ \text{V}&\text{opposing}&0\ \text{V}\\4\ \text{V}&4\ \text{V}&\text{aiding}&8\ \text{V}\\6\ \text{V}&4\ \text{V}&\text{opposing}&2\ \text{V}\\\end{array} V a 4 V 4 V 6 V V b 4 V 4 V 4 V mode opposing aiding opposing V out 0 V 8 V 2 V
Opposed dot polarity subtracts equal winding voltages
The polarity row cites two distinct winding sources; it cannot cite the same voltage source twice.
4 V + ( − 4 V ) = 0 V but aiding gives 8 V 4\ \text{V}+(-4\ \text{V})=0\ \text{V}\quad\text{but aiding gives}\quad8\ \text{V} 4 V + ( − 4 V ) = 0 V but aiding gives 8 V Dot polarity contrast Opposing and aiding rows use the same two checked windings. Np 1 Ns 1 dPhi 4 Wb dt 1 s Vp 4 V Vs 4 V mode aiding Np 1 Ns 1 dPhi 4 Wb dt 1 s Vp 4 V Vs 4 V mode aiding V1 4 V V2 4 V mode opposing Vout 0 V V1 4 V V2 4 V mode aiding Vout 8 V