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’.
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?
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
State any two sources of errors in the meter-bridge experiment. Explain how they can be minimized.
Four resistances 4 โฆ, 8โฆ, Xโฆ and 12โฆ are connected in a series to form Wheatstone’s network. If the network is balanced, the value of X is ______.
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 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 ______
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 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 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 ______.
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?
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 ______.
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 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 ______.
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 ____________.
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 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 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 ______
In the meter bridge experiment, a null point was obtained at a distance of โ 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 meter bridge experiment, to minimize an error due to contact resistance, ______
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 ______.
The current through 1 `Omega` resistance in the following circuit is ______.
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 ______
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 ______.
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.
In the given circuit, if I = 100 mA and I1 = I4 = 60 mA, the currents I3 and I5 are ______.
Draw a neat labelled diagram to determine unknown resistance using a meter bridge.
Draw a neat labelled diagram of Kelvin's meter bridge circuit for the measurement of galvanometer resistance.
In the given Wheatstone's network, what should be the value of R for the network to be balanced?
