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 gives
and
(1) then gives
Then
and