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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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What should be the value of R in the figure for which the current in it is zero?
State any two sources of errors in the meter-bridge experiment. Explain how they can be minimized.
Explain with a neat circuit diagram. How you will determine the unknown resistances using a meter bridge.
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?
ln the metre bridge experiment, one metre long wire acts as ____________.
The resistances in left and right gap of a metrebridge are 20 `Omega` and 30 `Omega` respectively. When the resistance in the left gap is reduced to half its value, the balance point shifts by ______.
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 ______.
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 ____________.
In following figure, a current of 1.4 A flows towards the bridge circuit. The current in 2 n resistor is ______.
Which among the following resistances can be determined by a metre bridge?
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 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 ______
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When an unknown resistance 'X' is connected in the left gap of a meter bridge and a known resistance 'R' in the right gap, a null point is obtained at 40 cm from the left end. If a 2 Ω resistance is connected in series with 'X' the null point shifts towards the right by 10 cm, with some resistance in the right gap. The value of 'X' must be ______
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.
A resistance of 20 Ω is connected in the left gap of a meter bridge and an unknown resistance greater than 20 Ω is connected in the right gap. When these resistances are interchanged, the balance point shifts by 20 cm. The unknown resistance is ______.
Explain the use of Wheatstone's metre bridge to determine an unknown resistance.
Draw a neat labelled diagram of Kelvin's meter bridge circuit for the measurement of galvanometer resistance.
Four resistances 4Ω, 4Ω, 4Ω and 12Ω form a Wheatstone's network. Find the resistance which when connected across the 12Ω resistance will balance the network.
What is a post office box? How is the· unknown resistance measured using a post office box?
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 ______.
A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is:
What is the primary purpose of a Wheatstone bridge in electrical circuits?
What is the mathematical expression for the balance condition of a Wheatstone bridge?
Which of the following is NOT a characteristic of a balanced Wheatstone bridge?
What is the main usefulness of a balanced Wheatstone bridge?
Why is high accuracy achievable in Wheatstone bridge measurements?
What would happen if the galvanometer in a Wheatstone bridge were replaced with a voltmeter?
