Advertisements
Advertisements
Question
Explain with a neat circuit diagram how will you determine unknown resistance ‘X' by using meter bridge
Advertisements
Solution
A Metre bridge consists of a wire of uniform cross-section and one metre in length, stretched on a metre scale which is fixed on a wooden table. The ends of the wire are fixed below two L shaped metallic strips. A single metallic stripe separates the two L shaped strips leaving two gaps, a left gap and a right gap.
Usually, an unknown resistance X is connected in the left gap and a resistance box is connected in the other gap. One terminal of a galvanometer is connected to terminal C on the central strip, while the other terminal of the galvanometer carries the jockey (J). Temporary contact with the wire AB can be established with the help of the jockey. A cell of emf (ε) along with a key (K) and a rheostat (Rh) is connected between points A and B.
A suitable resistance R is selected from the resistance box. The jockey is brought in contact with AB at various points on the wire AB and the balance point (null point), D, is obtained. The galvanometer shows no deflection when the jockey is at the balance point.
Let the respective lengths of the wire between A and D, and that between D and C be lx and lR. Then using the conditions for the balance, we get
`"X"/"R" = ("R"_"AD")/("R"_"DB")`
where RAD and RDB are resistance of the parts AD and DB of the wire resistance of the wire. If l is length of the wire, ρ its specific resistance, and A its area of cross section then
∴ `"R"_"AD" = (rho l_"AD")/"A"` and `"R"_"DB" = (rho l_"DB")/"A"`
∴ `"X"/"R" = "R"_"AD"/"R"_"DC" = (rho l_"x"//"A")/(rho l_"R"//"A")`
∴ `"X"/"R" = l_"x"/l_"R"`
∴ X = `l_"x"/l_"R" xx "R"`
Therefore R, lx and lR, the value of the unknown resistance can be determined.
APPEARS IN
RELATED QUESTIONS
With the help of a labelled diagram, show that the balancing condition of a Wheatstone bridge is
`R_1/R_2 = R_3/R_4` where the terms have their usual meaning.
Four resistances 4 Ω, 8Ω, XΩ and 12Ω are connected in a series to form Wheatstone’s network. If the network is balanced, the value of X is ______.
The current which flows in a galvanometer of Wheatstone bridge is directly proportional to ______
With resistances P and Q placed in the left and right gaps of a metre bridge, the balance point divides the wire in the ratio of 1/3. When P and Q are increased by 40 n each. the balance point divides the wire in the ratio of 3/5. The values of P and Q will be respectively, ______
In a Wheatstone bridge, when the potentials at points B and D are the same, then the current through the galvanometer ______
In the circuit shown, a metre bridge is in its balanced state. The metre bridge wire has a resistance 0.1 ohm/cm. The value of unknown resistance X and the current drawn from the battery of negligible resistance are ____________.
With a resistance of 'X' in the left gap and a resistance of 9 Ω in the right gap of a meter bridge, the balance point is obtained at 40 cm from the left end.
In what way and to which resistance 3 Ω resistance be connected to obtain the balance at 50 cm from the left end?
The metre bridge works on the principle of ______.
In the metre bridge experiment shown in the figure, the balance length AC corresponding to null deflection of the galvanometer is x. What would be the balance length if the radius of the wire AB is doubled?
On interchanging the resistances, the balance point of a metre bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k`Omega`. How much was the resistance on the left slot before interchanging the resistances?
ln the metre bridge experiment, one metre long wire acts as ____________.
In the Wheatstone bridge, (shown in the figure) X = Y and A > B. The direction of the current between a and b will be ____________.
When the value of R in the balanced Wheatstone bridge, shown in the figure, is increased from 5 `Omega` to 7 `Omega`, the value of s has to be increased by 3 `Omega` in order to maintain the balance. What is the initial value of S?
In the network shown cell E has internal resistance r and the galvanometer shows zero deflection. If the cell is replaced by a new cell of emf 2E and internal resistance 3r keeping everything else identical, then ______.
Which among the following resistances can be determined by a metre bridge?
In the measurement of a resistance by the Wheatstone bridge, the known and the unknown resistance are interchanged to eliminate ____________.
In a balanced metre bridge, 5 Ω is connected in the left gap and R Ω in the right gap. When R Ω is shunted with equal resistance, the new balance point is at 1.6 I1 where 'I1' is the earlier balancing length. The value of 'I1' is ______
The resistances in left and right gap of a meter-bridge are 3 `Omega` and 5 `Omega` respectively. When the resistance in the left gap is increased by 10%, the balance point shifts nearly by ______.
A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l1 = 2.9 cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?
The measurement of an unknown resistance R is to be carried out using Wheatstones bridge (figure). Two students perform an experiment in two ways. The first students takes R2 = 10 Ω and R1 = 5 Ω. The other student takes R2 = 1000 Ω and R1 = 500 Ω. In the standard arm, both take R3 = 5 Ω. Both find R = `R_2/R_1 R_3` = 10 Ω within errors.
- The errors of measurement of the two students are the same.
- Errors of measurement do depend on the accuracy with which R2 and R1 can be measured.
- If the student uses large values of R2 and R1, the currents through the arms will be feeble. This will make determination of null point accurately more difficult.
- Wheatstone bridge is a very accurate instrument and has no errors of measurement.
With an unknown resistance X in the left gap and a resistance of 30 Ω of the gap of a metre bridge, the null point is obtained at 40 cm from the left end of the wire. Find the unknown resistance. Also, find the shift in the null point when resistance in each gap is shunted by a resistance of 8 Ω.
What is a post office box? How is the· unknown resistance measured using a post office box?
Write balancing condition of a Wheatstone bridge.
