Advertisements
Advertisements
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.
Obtain the balancing condition in the case of Wheatstone’s network.
Advertisements
Solution
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`
APPEARS IN
RELATED QUESTIONS
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:
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
In a meter bridge, two unknown resistances R and S, when connected between the two gaps, give a null point is 60 cm from one end. What is the ratio of R and S?
Four resistances 6โฆ, 6โฆ, 6โฆ and 18โฆ form a Wheatstone bridge. Find the resistance which connected across the 18โฆ resistance will balance the network.
Explain with a neat circuit diagram. How you will determine the unknown resistances using a meter bridge.
In a meter bridge, the balance point is found to be at 39.5 cm from the end A when the resistor R is 12.5 โฆ (right gap).
a) Determine the resistance of X (left gap).
b) Determine the balance point of the bridge if X and R are interchanged?
c) What happens if the galvanometer and cell are interchanged at the balance point of the bridge?
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 ______
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?
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?
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 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?
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 the measurement of a resistance by the Wheatstone bridge, the known and the unknown resistance are interchanged to eliminate ____________.
In the meter bridge experiment, the null point is obtained at a distance of โ 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 meter bridge experiment, to minimize an error due to contact resistance, ______
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 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 ______.
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 โฆ and R1 = 5 โฆ. The other student takes R2 = 1000 โฆ and R1 = 500 โฆ. In the standard arm, both take R3 = 5 โฆ. Both find R = `R_2/R_1 R_3` = 10 โฆ 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.
The figure below shows a balanced Wheatstone network. If it is disturbed by changing P to 22Ω, then which of the following steps will bring the bridge again to a balanced state?
- 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.
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.
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)
The current passing through the battery in the given circuit 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 ______.
