## APPARATUS REQUIRED

i) Carey foster bridge

ii) Thick copper strips

iii) Fractional resistance box

iv) Connecting wires

v) Resistance

vi) A Jockey

vii) A sensitive galvanometer

viii) A cell

xi) A key.

## THEORY

Carey foster Bridge is an improved form of meter bridge. To increase the effective length of the meter bridge two more gaps are provided. Rest of the construction is similar to the meter bridge as shown in figure below. Here, P&Q are two ratio arms and X and Y are resistors in which Y can be known from a fractional resistance box. The unknown low resistance x can be determined as follow .If p is resistance per unit length that is, ohm 1 cm of the wire α_{1} and α_{2} respectively are the end resistance at a and b and a balance point is obtained at B where aD=l_{1}

Then,

P/Q = X+l_{1}p+α_{1} / Y(100-l_{1})p+α_{2} ………..(i)

If x and Y are interchanged and the balanced point is obtained at distance l2 from a Then we get,

P/Q = Y+l_{2}p+α_{1} / X+(100-l_{2})p+α_{2} ………..(ii)

Comparing equation (1) and (2) we get,

X+l_{1}p+α_{1} / Y+(100-L_{1})p+α_{2} = X+l_{2}p+α_{1} / Y+(100-l_{2})p+α_{2}

Adding 1 on both sides

X+l_{1}p +α_{1} / Y+(100-l_{1}) P+α_{2} = Y +l_{2}p+α_{1}+X+(100-l2)p+α_{2} / X+(100-l_{2})+α_{2}

Y+(100-l)p+α_{2} = X+(100-l_{2})p+α_{2}

Y-X = (l_{3}-l_{2})p

X= Y-(l_{3}-l_{2})p

## PROCEDURE

i) Complete the circuit as shown in the given diagram-Make the gaps 1, 2, 3 and 4 on the bridge. If necessary, clean the ends of connecting wire and the thick copper strip with a sand paper.

ii) Connect two equal resistance P and Q in inner gaps 2 and 3. If P and Q are two resistance boxes, take out 5 ohms flags from the either and make all other plugs tight.

iii) Without taking out any play from the frictional resistance box adjust the position of the Jockey to obtain a balance point and note the reading length aD = x

iv)Take out the plug from the jockey and k and again interchange x and Y. Now take out 0.1 ohm plug from tractional resistance Y and after again interchanging x and y.

v) Repeat the observation with the values of x equal 0.2, 0.3, 0.4 and 0.5 ohm etc.

vi) Remove the copper stripe and connect by a short thick Copper wire or metal bar keeping resistance in the fractional and resistance box zero.

vii) Repeat the observation by taking 0.1, 0.2, 0.3,0.4 and 0.5 ohm resistance from the fraction resistance box.

## OBSERVATION

Determination of ρ the resistance per cm of the bridge wire, balanced point with Y zero in the left gap(x)=45cm

Balanced point with Y zero and in the right gap (Y) = 46.8cm

Therefore, Correction = x-y = 46.8-45 =1.8cm

S.N | X | Y | Position of balance point with copper strip left gap(l_{1}) | Position of balance point with copper strip right gap(l_{2}) | shift (l_{1}-l_{2}) | Resistance ρ=1/α per cm | Correct shift d= (l_{1}-l_{2})-ρl | |

1 | 0 | 0 | 45 | 46.8 | 1.8 | 0 | 0 | |

2 | 0 | 0.1 | 48.1 | 44.6 | 3.5 | 0.05 | 1.7 | Mean R= 0 ohm |

3 | 0 | 0.2 | 48.6 | 39 | 9.6 | 0.01 | 7.8 | |

4 | 0 | 0.3 | 49.8 | 41.5 | 7.7 | 0.05 | 5.9 | |

5 | 0 | 0.4 | 46 | 39.5 | 6.6 | 0.08 | 48 | |

6 | 0 | 0.5 | 48.5 | 37.5 | 11 | 0.05 | 9.2 |

Determination of unknown new resistance.

S.N. | Y ohm | Position of balance point with unknown resistances left gap | Position of balance point with unknown resistances right gap | Shift (l_{1}-l_{2}) cm | Correct shift d= (l_{1}-l_{2})ρ | Unknown resistance Y= ρd |

1 | 0 | 46.3 | 51.5 | 5.2 | 4.4 | 0 |

2 | 0.1 | 46.7 | 50.7 | 4 | 2.2 | 0.167 |

3 | 0.2 | 47 | 48.9 | 1.5 | 0.7 | 0.198 |

4 | 0.3 | 50.7 | 47.4 | 3.3 | 1.4 | 0.213 |

5 | 0.4 | 51.1 | 45.4 | 5.7 | 3.6 | 0.112 |

6 | 0.5 | 53.8 | 44.5 | 9.4 | 7.6 | 0.22 |

Mean Y = 0.1370 Ohms

## RESULT

The value of ρ the resistance per cm of the bridge wire is 0.04 ohm cm and unknown resistance 0.1370 Ohms.

## PERCENTAGE ERROR

Actual value of the given resistance (ρ) = 2 ohms

Obtain value of the low resistamer (O) = 0.5 ohms

Therefore: % error = ρ-0/ρ x100%

= 2-0.5/2 x100%

= 7.5 %

## PRECAUTIONS AND SOURCE OF ERROR

i) The ends of the connecting wires should be clean and should be firmly secured in the binding terminal.

ii) A plug bey should be used in the call circuit and the Current should be allowed to flow only for the time reading are taken.

iii) The jockey should be pressed gently and instantly.

iv) The use of a rheostat to obtain the ratio arms P and Q whose values should nearly be equal.

V) To Avoid any induction effects the cell circuit should be completed first and then the galvanometer circle.