Mathematics Revision of Current Electricity For NDA : Part - 2
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Kirchhoff's Laws

Sometimes complex electric circuits cannot be reduced to simple series parallel combination, for analysing such circuits Kirchhoff's gave two laws. Which are as follows

(i) `text(Junction law )` The algebraic sum of the current flowing into any junction is zero.

Thus, `sum I_text(junction) = 0`

(ii) `text( Loop law )` The algebraic sum of the potential difference is any closed loop is equal to zero.

Thus , `sum Delta V = 0 => sum E + RI = 0`

`Delta E = - sum RI`

`text(Wheat stone's Bridge )`

It is an arrangement of four resistances making a closed circuit The resistance of given conductor can be determined with its help. When there is no deflection in the galvanometer, then

`P/Q = R/S`

In this case `V_B = V_D` and the bridge will be balanced

Different Measuring Devices

• `text(Ammeter)` Ammeter is a device which is used to measure the electric current in a circuit.
Ammeter is always connected in series with the current source. It has very low resistance.

• `text(Voltmeter) ` Voltmeter is a device which is used to measure the potential difference across the ends of a conductor. Voltmeter is always connected in parallel. It has very high resistance.

•`text(Galvanometer)` Galvanometer is a device used to detect the presence of the electric current in a circuit.

To convert galvanometer into ammeter a low resistance wire called shunt is connected in parallel with the galvanometer.

Resistance of shunt, `S = (i_g G)/(i - i_g)`

where `G =` resistance of galvanometer,

`i =`range of ammeter

and `i_g =` safe current for galvanometer coil

To convert galvanometer into voltmeter a high resistance `(R)` is connected in series with the galvanometer, `R = V/i_g -G`

where , `V =` range of voltmeter

Heating Effect Of Electric Current

Whenever the electric current is passing through a conductor, then it becomes hot after some times. This indicates that electric energy is being converted into heat energy. This effect is known as heating effect of current of Joule heating effect.

`H = W/(4.2) = (VIt)/(4.2) = (V^2t)/(4.2R) = (I^2Rt)/(4.2)`

`text(Electrical Power)`

The rate at which work is done by the source of emf in maintaining the effect of current in a circuit is called electric power of the circuit.

`P =VI = V^2/R = I^2R`

SI unit of Power is watt.

`text(Electrical Energy)`

The total work done by the source of emf is maintaining the electric current in the circuit for a given time is called electrical energy consumed in the circuit. Sl unit of electric energy is joule but another unit is watt-hour.

`text(Kilowatt-hour (kWh))`

It is bigger unit of electric energy. lt is known as Board of Trade Unit (BTO).

1 kWh = P(in kW) x t (in hour)
1 kWh = 1000 X 3600
1 kWh `= 3.6 xx 10^6` Joule

The electric energy consumed in kWh is given by

`W = (V xx I xx t )/1000`

Thermoelectric Effect

The phenomenon of production of electricity with the help of heat is called thermoelectricity and this effect is called thermoelectric effect.

`text(Seebeck Effect)`

When a temperature difference is produced across the junctions of two different materials, then a current starts flowing in the couple of wires, without the presence of any external battery.
The emf causing this flow is called thermo emf and this effect is known as thermoelectric effect or Seebeck effect.

`text(Peltier Effect)`

The absorption or evolution of heat at a junction of two dissimilar metals, when current is passed through is known as Peltier effect.

Peltier coefficient, `pi = T (dE)/(d theta)`

`text(Thomson Effect)`

The absorption or evolution of heat along the length of a wire when current is paused through a wire whose ends are kept at different temperatures is known as Thomson effect.

Thomson coefficient `sigma = -T (dS)/(d theta)`

Chemical effect of Electricity

The most common chemical effect of current electricity is electrolysis just like solids, some liquid also conduct electricity. Such liquid arc called electrolytes. When electric current passes through an electrolyte is decomposes into its constituents.

`text(Faraday's laws of Electrolysis)`

`(i) text(First law :)` The amount of substance deposited or liberated in electrolysis is directly proportional to the charge flowing through the electrolyte. Amount deposited or liberated, `m = zq` or `m =zit` where, `z =` electrochemical equivalent of the substance

`(ii) text(Second law: )` If same amount of current is passed through different electrolytes for same time, then the ratio of masses of tl:.e substance liberated at respective electrodes is equal to the ratio of their chemical equivalents.

`m_1/m_2 = E_1/E_2`

where `E_1` and `E_2 =` chemical equivalents of the first and second subtances.

or `z_1/z_2 = E_1/E_2`

`text(Faratday Constant)` ( F)

The quantity of charge required to liberate one gram equivalent of a substance is called Faraday constant (F).

`F =E/A => F = 96500` coulomb or `F = Ne`

where , `N =` Avogadro's number and `e =` electronic charge

 
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