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Current Electricity
Ohm’s law is insufficient to calculate currents and
voltages in complicated circuits. Containing more
than one energy sources and current carrying
branches. Thus Kirchhoff’s laws are used.
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Kirchoff’s Laws
1. Kirchoff’s Current Law ( KCL ) / Junction Law
Statement
Algebraic sum of the currents flowing through any
node is always zero. i.e. ΣI= O
∙ Node is a point, where more than 2
connections meet. It is also known as
junction.
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Convention
∙ The currents flowing towards the node are
considered positive.

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∙ The currents leaving / moving away from the
node are considered negative.
i.e. I1 + I2 – I3 – I4 – I5 = 0
∴ I1 + I2 = I3 + I4 + I5
 Current is the amount of charge flowing per
second.
 ( I1 + I2 ) is the amount of change approaching the
node in 1sec and (I3 + I4 + I5) is the amount of change
leaving the junction in 1sec.
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 The junction is neither consuming nor adding the
change.
2. Kirchoff’s Voltage Law (KVL) / Theorem of
loop
Statement
Algebraic sum of e.m.f’s along any closed loop is
equal to sum of the products of current and
resistance in that part of the loop. i.e. ΣE = ΣIR
∙ Applicable to any loop individually.
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Convention
 Current flowing in the opposite direction in which
the loop is traced is considered positive. The
current in the same direction is considered
negative.

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 The e.m.f. which tends to circulate current in the
same direction in which the loop is stretched is
considered positive and the e.m.f. which tends to
circulate current in the opposition direction is
considered negative.
There are 3 loops.
1. ABCDEFA
2. ABCFA
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3. FCDEF

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For loop, ABCDEFA
- E1 +I1 R1 - I2 R2 + E2 - I2 R3 + I1R4 = O
∴ E2-E1= I2 (R2 + R3) – I1 (R1 + R4).
i.e. ΣE = ΣIR
Justification
 e.m.f. is the energy spent by the cell to circulate
unit charge once through the entire loop.
 Product of current and resistance is the voltage
across the resistor which is the energy spent to
circulate unit charge once through that resistor.
 Hence L.H.S of the equation gives the total
amount of energy supplied by the cells & R.H.S is
the total amount energy used by the loop.

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According to the law of conservation of energy,
these energies are equal.
i.e. ΣE = ΣIR
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