

Complex
Circuits 

Sometimes we encounter circuits where simplification by series
and parallel combinations is impossible. Consequently, Ohm's
law cannot be applied to solve such circuits. This happens when
there is more than one source of e.m.f. in the circuit or when
resistors are connected in a complicated manner. such circuit
are called complex circuits. We shall discuss two such circuits
by way of illustration. 

(I) Fig (a) shows a circuit
containing two source of e.m.f. E_{1} and E _{2
} are three resistors. This circuit cannot be solved
by seriesparallel combinations. Are resistor R _{1}
and R _{3 }in series? Not quite, because same current
does not flow in them.



Fig (a) 

(II) Fig (b) shows another circuit where we cannot solve the
circuit by using series and parallel combinations. Through
this contains one source of e.m.f. (E), it cannot be solved
by using series and parallel combinations. Are resistors R
_{1} and R _{2 } are neither in series nor
in parallel, same is true for other pair of resistors. 


Fig
(b) 

In
order to solve such complex circuits, Gustav Kirchhoff gave
two laws , known as Kirchhoff's laws. 
