1. Kirchoff's 1^{st} law/ Kirchoff's current law/ Kirchoff's
junction law:

The algebric sum of current at a junction is always zero. i.e. ΣI=0

Sign convention If the current is towards the junction point, then it is taken as +ve and
if the current is away from the junction point, then it is taken as -ve.

In figure at junction A, Applying kirchoff's
1^{st} law ΣI=0 I
_{1}+(-I_{2})+I_{3}+(-I_{4}) = 0 I
_{1}-I_{2}+I_{3}-I_{4}=0 I
_{1}+I_{3}=I_{2}+I_{4}

This means the sum of total current incoming to
junction is equal to the sum of total current moving away from the junction. This law
is accordance with the conservation of charge.

2. Kirchoff's 2^{nd} law/ Kirchoff's voltage law/ Kirchoff's
loop law:

The algebric sum of EMF's and P.D.'s at a loop is always zero. ΣE + ΣIR = 0
This law follows the conservation of energy.

Sign convention If the direction of taken loop touches the +ve terminal of the cell then
it's emf is taken as +ve otherwise -ve. If the direction of current is in the direction of
taken loop, then the current is taken as +ve otherwise -ve.

In the figure: taking the loop FCBAF ΣE +
ΣIR = 0 [E
_{2} + (-E_{1})] + [-I_{2}R_{2} + I
_{1}R_{1}]=0 E
_{2}-E_{1}= I_{2}R_{2} - I
_{1}R_{1} E
_{1} - E_{2}= I_{1}R_{1} - I
_{2}R_{2}

Wheatstone Bridge Circuit

It is the combination of four resistors in which three of them is known and one is unknown. The combination of
resistor are as shown in figure. In the figure P,Q and R are known resistance and X is unknown. At the
balance condition, that is for null deflection of galvanometer, we can write, P/Q = X/R This condition
is called wheatstone bridge condition.

Wheatstone Bridge Condition:

The wheatstone bridge circuit consist of four resistance P,Q,X and R as shown in figure. Let I
_{1},I_{1},I_{1},I_{1} are the current through resistor P,X,Q,R
respectively. A galvanometer of resistance R_{g} is connected between the terminal B and D through
which a current I
_{g} flow.

Applying the kirchoff's current law at a junction point B and D. The value of
current through a resistance Q and R is: I
_{3}= I_{1}- I_{g} I
_{4}= I_{2} + I_{g} and taking the loop ABDA and applying kirchoff's voltage
law: ΣE + ΣIR = 0 or, 0 + I_{1} x P + I_{g} x R_{g} - I
_{2} x X = 0 at a balance condition (null deflection condition) I
_{g} = 0, we get, I
_{1}P - I_{2} x X = 0 I
_{1}P = I_{2}X
<-------- (i)
Taking the loop BCDB and applying kirchoff's voltage law, ΣE + ΣIR = 0 0 + I_{3} x Q -
I_{4} x R - I
_{} x R_{g} = 0 at balance condition (I
_{g}=0) we get, I
_{3} x Q = I_{4} x R I
_{1}Q = I_{2}R
<------ (ii)
dividing equation (i) and equation (ii) we get, P/Q = X/R which is the required wheatstone
bridge condition.

Potentiometer It is a device which is used to measure the emf of the cell. Compare the EMF of the two cell
and determine the internal resistance of a cell. It consist of 10 m long uniform cross
section wire made up of constant or Eureka which is divided to equal segment. Each segment is 1 m long is placed
over a wooden board by the help of copper stripes. A meter scale is placed in the lower copper's
part of the wooden board provided two way scale.

Principle of Potentiometer:

On sliding the jockey over a potentiometer wire
AB a null point is obtained at a point 'C' of length 'l_{ac}' . from the ohm's
law,
V= IR_{ac}
<-------- (i)
I= current through the potentiometer wire. R
_{ac}= (ρ x l_{ac})/A where, ρ= resistivity of the material of the potentiometer wire.
A= cross sectional area. from equation (i) and (ii), V= I. (ρ x l
_{ac})/A
V= k. l_{ac} where, k= Iρ/A = constant V ∝ l
_{ac} V ∝ l

When a constant current is passed through the potentiometer then the
potential dropped across any portion is directly proportional to the length of that portion.

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