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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’.
Explain with a neat circuit diagram how will you determine unknown resistance ‘X' by using meter bridge
What should be the value of R in the figure for which the current in it is zero?
Obtain the balancing condition for the Wheatstone bridge arrangements as shown in Figure 4 below:
Choose the correct:
Four resistances 10 Ω, 10 Ω, 10 Ω and 15 Ω form a Wheatstone’s network. What shunt is required across 15 Ω resistor to balance the bridge
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The metre bridge works on the principle of ______.
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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 ______.
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In the given circuit, if I = 100 mA and I1 = I4 = 60 mA, the currents I3 and I5 are ______.
Explain the use of Wheatstone's metre bridge to determine an unknown resistance.
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Draw a neat labelled diagram of Kelvin's meter bridge circuit for the measurement of galvanometer resistance.
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)
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?
In the given Wheatstone's network, what should be the value of R for the network to be balanced?
Write balancing condition of a Wheatstone bridge.
