Chapter 10: Kirchhoff’s Law

Kirchhoff came up with two laws concerning conservation in electrical circuits.

First law

It states that the sum of currents entering any point in a current is equal to the sum of the currents leaving that same point (conservation of charge). Electric charge is conserved in the circuits, all charge that arrive at a point must leave it.

In the figure,

Current going in = current going out

I1= I2 + I3 + I4

 

Second Law

It states that the sum of the e.m.f.s around any loop in a circuit is equal to sum of the p.d.s around the loop.

In the figure,

Energy givers = energy takers

ɛ = pd1 + pd2 + pd3 + pd4

Combinations of Resistors

Resistors in series

If the three resistors R1, R2 and R3 are connected in series. Then according to Kirchhoff’s first law; the p.d. V across the combination is equal to the sum od p.d.s across the two resistors:

V = V1 + V2 + V3

Since V = IR,

So, IR = IR1 + IR2 + IR3

Canceling common factors,

R = R1 + R2 + R3 ………..

Resistors in parallel

 

When three resisters of resistance R1, R2 and R3 are connected in parallel. Using Kirchhoff’s law,

I = I1 + I2 + I3

We know, I =

So, substituting the value of I and cancelling the common factor V we get,

1/R=1/R1+1/R2+1/R3 ………

 

Ammeters have low resistance and are connected in series in a circuit.

Voltmeters have a high resistance and are connected in parallel in a circuit.

 

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