- A limited ammount of current can be drawn from a single cell or battery

- There are situations where single cell fails to meet the current requirement in a circuits

- To overcome the problem cells can be grouped in series and in parallel combinations or mixed grouping of cells is done in order to obtain a large value

of electric current

- Figure below shows the two cells of emf's E
_{1}and E_{2}and internal resistance r_{1}and r_{2}respectively connected in series combination through external resistance

- Points A and B in the circuit acts as two terminals of the combination

- Applying kirchoff's loop rule to above closed circuit

-Ir_{2}-Ir_{1}-IR+E_{1}+E_{2}=0

or

I=E_{1}+E_{2}/R+(r_{1}+r_{2})

Where I is the current flowing through the external resistance R

- Let total internal resistance of the combination by r=r
_{1}+r_{2}and also let E=E_{1}+E_{2}is the total EMF of the two cells

- Thus this combination of two cells acts as a cell of emf E=E
_{1}+E_{2}having total internal resistance r=r_{1}+r_{2}as shown above in the figure

- Figure below shows the two cells of emf E
_{1}and E_{2}and internal resistance r_{1}and r_{2}respectively connected in parallel combination through external resistance

- Applying kirchoff's loop rule in loop containing E
_{1},r_{1}and R,we find

E_{1}-IR-I_{1}r_{1}=0 ------------------------(1)

Similarly applying kirchoff's loop rule in loop containing E_{2},r_{2}and R,we find

E_{2}-IR-(I-I_{1})r_{2}=0 ------------------------(2)

- Now we have to solve equation 1 and 2 for the value of I,So multiplying 1 by r
_{2}and 2 by r_{1}and then adding these equations results in following equation

IR(r_{1}+r_{2})+r_{2}r_{1}I-E_{1}r_{2}-E_{2}r_{1}=0

which gives

We can rewrite this as

E is the resulting EMF due to parallel combination of cells and r is resulting internal resistance.

- Wheat stone bridge was designede by british physicist sir Charles F wheatstone in 1833

- It is a arrangement of four resistors used to determine resistance of one resistors in terms of other three resistors

- Consider the figure given below which is an arrangement of resistors and is knowns as wheat stone bridge

- Wheatstone bridge consists of four resistance P,Q,R and S with a battery of EMF E.Two keys K
_{1}and K_{2}are connected across terminals A and C and B and D respectively

- ON pressing key K
_{1}fisrt and then pressing K_{2}next if galvanometer does not show any deflection then wheatstone bridge is said to be balanced

- Galavanometer is not showing any deflection this means that no current is flowing through the galvanameter and terminal B and D are at the same

potential .THus for a balanced bridge

V_{B}=V_{D}

- Now we have to find the condition for the balanced wheatstone bridge .For this applying kirchoff's loop rule to the loop ABDA ,we find the relation

-I_{2}R+I_{1}P=0

or I_{1}P=I_{2}R --(a)

Again applying kirchoff's rule to the loop BCDB

I_{1}Q-I_{2}S=0

or I_{1}Q=I_{2}S --(b)

From equation a and b we get

I_{1}/I_{2}=R/P=S/Q

or

P/Q=R/S (12) - equation 12 gives the condition for the balanced wheatstone bridge

- Thus if the ratio of the resistance R is known then unknown resistance S can easily be calculated

- One important thing to note is that when bridge is balanced positions of cell and galvanometer can be exchanged without having any effect on the balance of the bridge

- Sensitivity of the bridge depends on the relative magnitudes of the resistance in the four arm of the bridge is maximum for same order of four resistance.

- Introduction
- |
- ElectroMotive Force(emf)
- |
- Internal Resistance of Battery (or cell)
- |
- Electric Energy and Power
- |
- Kirchoff's Rules
- |
- The junction Rule (or point rule)
- |
- The Loop Rule (or Kirchoff's Voltage Law)
- |
- Grouping of the cell's
- |
- Meterbridge (slide wire bridge)
- |
- Potentiometer
- |
- Comparison of EMF's of two cells using potentiometer
- |
- Determination of internal resistance of the cell

Class 12 Maths Class 12 Physics

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