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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.
Obtain the balancing condition in the case of Wheatstone’s network.
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Four resistances P, Q, R and S are connected to form a quadrilateral ABCD as shown in the following figure. A battery of emf ε along with a key, is connected between points A and C such that point A is at higher potential with respect to point C. A galvanometer of internal resistance G is connected between points B and D.
When the key is closed, current I flows through the circuit. It divides into I1 and I2 at point A. I1 is the current through P, and I2 is the current through S. The current I1 gets divided at point B. Let Ig be the current flowing through the galvanometer. The currents flowing through Q and R are respectively (I1 – Ig) and (I2 + Ig),
I = I1 + I2 ...(1)
Consider the loop ABDA. Applying Kirchhoff’s voltage law in the clockwise sense shown in the loop, we get
–I1P – IgG + I2S = 0 ...(2)
Applying Kirchhoff's voltage law to loop BCDB in a clockwise sense, we get,
–(I1 – Ig)Q + (I2 + Ig)R + IgG = 0 .....(3)
From these three equations (Eq. (1), (2), (3), we can find the current flowing through any branch of the circuit.
A special case occurs when the current passing through the galvanometer is zero. In this case, the bridge is said to be balanced. The condition for the balance is Ig = 0. This condition can be obtained by adjusting the values of P, Q, R and S. Substituting Ig = 0 in Eq. (2) and Eq. (3) we get,
–I1P + I2S = 0 ∴ I1P = I2S ...(4)
–I1Q + I2R = 0 ∴ I1Q = I2R ...(5)
Dividing Eq. (4) by Eq. (5), we get
`∴ (I_1 P)/(I_1 Q) = (I_1 S)/(I_2 R)`
`therefore P/Q = S/R`
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Four resistances 4Ω,8Ω,XΩ, and 6Ω are connected in a series so as to form Wheatstone’s
network. If the network is balanced, find the value of ‘X’.
Obtain the balancing condition for the Wheatstone bridge arrangements as shown in Figure 4 below:
State any two sources of errors in the meter-bridge experiment. Explain how they can be minimized.
Four resistances 4 тДж, 8тДж, XтДж and 12тДж are connected in a series to form Wheatstone’s network. If the network is balanced, the value of X is ______.
Four resistances 6тДж, 6тДж, 6тДж and 18тДж form a Wheatstone bridge. Find the resistance which connected across the 18тДж resistance will balance the network.
In conversion of moving coil galvanometer into an ammeter of required range, the resistance of ammeter, so formed is ______.
[S = shunt and G = resistance of galvanometer]
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, ______
Two wires A and B of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at 40 cm from left end. Diameters of the wire A and B are in that ratio 3 : 1. The ratio of specific resistance of A to the of B is ____________.
In a Wheatstone bridge, when the potentials at points B and D are the same, then the current through the galvanometer ______
In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?
In a metre bridge, the gaps are closed by two resistances P and Q and the balance point is obtained at 40 cm. When Q is shunted by a resistance of 10 Ω, the balance point shifts to 50 cm. The values of P and Q are ______
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?
In Wheatstone's bridge P = 7 ohm, Q = 12 ohm, R = 3 ohm and S = 8 ohm. How much resistance must be put in parallel to the resistance S to balance the bridge?
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?
In Wheatstone's network p = 2 `Omega` , Q = 2 `Omega`, R = 2 `Omega` and S = 3 `Omega`. The resistance with which S is to be shunted in order that the bridge may be balanced is ______.
A resistance of 5 `Omega` is connected in the left gap of a metre bridge and 15 `Omega` in the other gap. The position of the balancing point is ____________.
Two resistances prepared from the wire of the same material having diameters in the ratio 2 : 1 and lengths in the ratio 2 : 1 are connected in the left gap and right gap of Wheatstone's meter bridge respectively. The distance of the null point from the left end of the wire is ______
In the meter bridge experiment, the null point is obtained at a distance of тДУ from the left end. The resistance in the left and right gaps are halved and then interchanged. The new position of the null point is at ______
In the meter bridge experiment, a null point was obtained at a distance of тДУ from the left end. The values of resistances in the left and right gaps are doubled and then interchanged. The new position of a null point is ______
In a metre bridge experiment, the ratio of the left-gap resistance to right gap resistance is 2: 3. The balance point from the left is ______.
ln, a Wheatstone network, P = Q = R = 8 `Omega` and S is 10 `Omega`. The required resistance to be connected to S so that network is balanced is ______.
The current through 1 `Omega` resistance in the following circuit is ______.
The Wheatstone bridge is in a more balanced state when the ratio of arms P and Q is ______
A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100тДж. 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 тДж and R1 = 5 тДж. The other student takes R2 = 1000 тДж and R1 = 500 тДж. In the standard arm, both take R3 = 5 тДж. Both find R = `R_2/R_1 R_3` = 10 тДж 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.
- Assertion (A): The given figure does not show a balanced Wheatstone bridge.
- Reason (R): For a balanced bridge small current should flow through the galvanometer.
In the given circuit, if I = 100 mA and I1 = I4 = 60 mA, the currents I3 and I5 are ______.
Find the radius of the wire of length 25m needed to prepare a coil of resistance 25Ω. (Resistivity of material of wire is 3.142 x 10-7Ωm)
Write balancing condition of a Wheatstone bridge.
Two resistances are connected in two gaps of a meter bridge. The null point is obtained at 20 cm from zero end. A resistance of 15 is connected in series with smaller of the two. The null point shifts to 40 cm. The smaller resistance used in is ______.
In a Wheatstone’s bridge, three resistances P, Q and R connected in the three arms and the fourth arm is formed by two resistances S1 and S2 connected in parallel. The condition for the bridge to be balanced will be ______.
