**NEET Physics Notes Electrostatics-Kirchhoff s Laws and their Applications**

**Kirchhoff s Laws and their Applications**

**Kirchhoff s Laws and their Applications**

Sometimes complex electric circuits cannot be reduced to simple series parallel combination. For analysing such circuits Kirchhoff gave two laws, which are as follow

**Junction Law**

The algebraic sum of the currents flowing into any junction is zero. Thus,

**Sign Convention**

Current carrying into the junction is taken as positive while current going out is taken as negative.

**Loop Law**

The algebraic sum of the potential differences in any closed loop is equal to zero.

**Thus,**

**Sign Convention**

- In a loop when we traverse through a source in the direction from negative terminal to positive terminal, emf is considered positive.

And from positive to negative terminal, its is taken negative. - When we traverse a resistor in the assumed direction of current IR is taken as negative and in its reverse direction, IR is taken as positive. .
- Kirchhoffs first law is based on conservation of electric charge.
- Kirchhoffs second law is based on the conservation of energy.

**Wheatstone’s Bridge**

It is a sensitive arrangement to determine the value of an unknown resistance. The bridge is said to be balanced, if on switching the keys K_{1} and K_{2} there is no deflection in galvanometer. It is possible when V_{B} = V_{D}.

In balanced bridge Q and R can be interchanged without affecting the balance condition. Similarly, P and S can be interchanged. Moreover, cell and galvanometer may also be interchanged.

If an electric circuit resembles a balanced Wheatstone bridge, then resistance of branch BD may be ignored (or removed from the circuit) as no current is flowing through it.

**Meter Bridge**

A meter bridge is a practical arrangement to realise Wheatstone’s bridge.

If by sliding the tapping point a null point is obtained on bridge wire at point B, then in balanced condition.

**Potentiometer**

Potentiometer is an instrument which can be used for different electric measurements. It is commonly used to find emf of a given cell and to find internal resistance of a cell.

Here, AB is a long uniform resistance wire (length AB may be ranging from 1 m to 10 m). E_{0} is a battery whose emf is known supplying a constant current I for flow through the potentiometer wire. If R be the total resistance of potentiometer wire and L its total length, then potential gradient, i.e. fall in potential per unit length along the potentiometer will be

**Applications of Potentiometer**

The several applications of potentiometer are given below Determination of Emf of a Cell If with a cell of emf E on sliding the contact point we obtain zero deflection in galvanometer G when contact point is at / at a length 1 from the end where positive terminal of cells have been joined, then fall in potential along length 1 is just balancing the emf of cell. Thus, we have E = kl

Comparison of Emfis of Two Cells If with a given potentiometer arrangement we obtain balancing lengths l_{1} and l_{2} for cells of emfs

E_{1} and E_{2}, then

Determination of Internal Resistance of a Cell The arrangement is shown in figure. If the cell E is in open circuit and balancing length is l_{1} then

But if by inserting key K2 circuit of cell is closed, then potential difference V is balanced by a length l_{2} of potentiometer, where **V = kl2**

**Internal resistance of cell**

**Galvanometer**

It is a sensitive instrument used to detect and measure very small currents even of the order of few micro ampere.

In a common moving coil galvanometer deflection obtained is directly proportional to the current passed, i.e.

Figure of merit of a galvanometer is defined as the current which gives one division deflection in galvanometer.

**Ammeter**

An ammeter is a device used to measure current directly in ampere or its submultiples. An ammeter is always connected in series with the element, current through which is to be measured.

Resistance of an ammeter is extremely small. For an ideal ammeter its resistance is zero.

A galvanometer may be converted into an ammeter of rating I by connecting a suitable low resistance (known as shunt S) in parallel with the galvanometer. Value of shunt resistance

where, I*g* = maximum safe current (full scale deflection current) which can be passed through galvanometer,

I – range of ammeter, G = resistance of galvanometer.

If J = n*Ig,* then shunt

The equivalent resistance of ammeter

**Voltmeter**

A voltmeter is a device used to measure potential difference across a circuit element in volts. A voltmeter is always connected in parallel to the element. Resistance of a voltmeter is quite high. For an ideal voltmeter its resistance is taken as infinite.

A galvanometer may be converted into a voltmeter by connecting a suitable high resistance R in series with galvanometer.

Value of series resistance

where V = range of voltmeter.

The equivalent resistance of **voltmeter = G + R.**