<P> The second law applied to the closed circuit s gives </P> <Dl> <Dd> − R 3 i 3 − E 2 − E 1 + R 2 i 2 = 0 (\ displaystyle - R_ (3) i_ (3) - (\ mathcal (E)) _ (2) - (\ mathcal (E)) _ (1) + R_ (2) i_ (2) = 0) </Dd> </Dl> <Dd> − R 3 i 3 − E 2 − E 1 + R 2 i 2 = 0 (\ displaystyle - R_ (3) i_ (3) - (\ mathcal (E)) _ (2) - (\ mathcal (E)) _ (1) + R_ (2) i_ (2) = 0) </Dd> <P> Thus we get a system of linear equations in i 1, i 2, i 3 (\ displaystyle i_ (1), i_ (2), i_ (3)): </P>

Kirchhoff's law applicable for ac or dc