Electric circuits generally consist of a number of resistors and
cells interconnected sometimes in a complicated way. The formulae we have
derived earlier for series and parallel combinations of resistors are not
always sufficient to determine all the currents and potential differences in
the circuit. Two rules, called Kirchhoff’s rules, are very useful for analysis
of electric circuits.
KIRCHHOFF’S RULES
Kirchhoff’s first Law or
Kirchhoff’s Junction Law or Kirchhoff’s current law: Algebraic sum of the currents meeting at a
junction in a closed circuit is zero.
According to law total,
charge at the junction is zero i.e. -I1 + (-I2) + I3
+ (-I4) + I5 = 0
∑ I = 0
First law supports law of
conservation of charge. At
time t current coming is equal to current going i.e.
I1t = I2t => q1=q2
Sign convention: current coming towards junction is positive and
current going away is negative.
Kirchhoff’s laws are applicable to AC as well as DC circuits.
Kirchhoff’s second Law or
Kirchhoff’s loop Law or Kirchhoff’s voltage law: Algebraic sum of changes in potential around any
closed path of electric circuit (or closed loop) involving resistors and cells
in the loop is zero i.e.
∑∆V = 0, also ∑ ε = ∑ IR
In loop ABEFA, according to
Kirchhoff’s rule
I3R2 +
I1R1 – ε1 =0, or ε1 = I3R2
+ I1R1
In loop ABCDEFA, according to
Kirchhoff’s rule
ε2 - I3R2
+ I1R1 – ε1 =0, or ε1 - ε2 = I1R1 - I3R2
Second law supports law of conservation of energy. We can also say it follows that electrostatic
fore is a conservative force and work done in closed loop is zero.
Sign convention: e.m.f of a cell is taken negative if one moves in
the direction of increasing potential and is taken as positive if one moves in
the direction of deceasing potential.
Product of resistor and current is taken as positive if current
coming from positive terminal and is taken as negative if current is coming
from negative terminal.
∑ε=∑IR is true when there is no capacitor in the circuit.
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