Kirchoff's Laws are used to find currents through components in circuits and voltages across components in circuits.

Kirchoff's 1^st Law

The current into a circuit junction equals the current out.

Kirchoff's 2^nd Law

The net voltage around a circuit loop is zero.

We can apply the laws to the diagram below.

Applying the 1^st Law at A gives(1)

Applying the 2^nd Law

for loop 1 gives(2)

for loop 2 gives(3)

for loop 3 gives(4)

Substitute (1) into (2) and (3) to give

(5)

(6)

Solving (5) and (6) simultaneously givesand(1) then gives

Thenand