Advertisements
Advertisements
प्रश्न
Obtain the condition for bridge balance in Wheatstone’s bridge.
Obtain the balancing conditions in the case of Wheatstone’s bridge.
Advertisements
उत्तर १
An important application of Kirchhoff’s rules is the Wheatstone Bridge. It is used to compare resistances and also helps in determining the unknown resistance in an electrical network. The bridge consists of four resistances, P, Q, R, and S, connected. A galvanometer G is connected between the points B and D. The battery is connected between points A and C. The current through the galvanometer is IG, and its resistance is G.
Wheatstone’s bridge
Applying Kirchhoff’s current rule to junction B,
I1 – IG – I3 = 0 ...(1)
Applying Kirchhoff’s current rule to junction D,
I2 + IG – I4 = 0 ...(2)
Applying Kirchhoff’s voltage rule to loop ABDA,
I1P + IGG – I2R = 0 ...(3)
Applying Kirchhoff’s voltage rule to loop ABCDA,
I1P + I3Q – I4S – I2R = 0 ...(4)
When the points B and D are at the same potential, the bridge is said to be balanced. As there is no potential difference between B and D, no current flows through the galvanometer (IG = 0).
Substituting IG = 0 in equations (1), (2), and (3), we get
I1 = I3 ...(5)
I2 = I4 ...(6)
I1P = I2R ...(7)
Substituting equations (5) and (6) in equation (4),
I1P + I1Q – I2R = 0
I1(P + Q) = I2 (R + S) ...(8)
Dividing equation (8) by equation (7), we get
`(P + Q)/P = (R + S)/R`
`11 + Q/P = 1 + S/R`
⇒ `Q/P = S/R`
`P/Q = R/S` ...(9)
This is the bridge balance condition. Only under this condition, the galvanometer shows null deflection. Suppose we know the values of two adjacent resistances; the other two resistances can be compared. If three of the resistances are known, the value of the unknown resistance (the fourth one) can be determined.
उत्तर २
In a Wheatstone bridge at balance, no current flows through the galvanometer. Hence, the potential at junction points is equal.
Let resistances be P, Q, R, and S.
By using the given condition:
`P/Q = R/S`
⇒ PS = QR
Notes
Students can refer to the provided solutions based on their preferred marks.
APPEARS IN
संबंधित प्रश्न
Kirchhoff's voltage law and current law are respectively in accordance with the conservation of .................................. .
- charge and momentum
- charge and energy
- energy and charge
- energy and momentum
Kirchhoff's junction law is equivalent to .............................
(a) conservation of energy.
(b) conservation of charge
(c) conservation of electric potential
(d) conservation of electric flux
Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.
Determine the current in each branch of the network shown in figure.
Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?
The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for
- the current draw from the cell and
- the power consumed in the network.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/3) Ω?
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/5) Ω?
Determine the equivalent resistance of networks shown in Fig.
State Kirchhoff's rules for an electric network. Using Kirchhoff's rules, obtain the balance condition in terms of the resistances of four arms of Wheatstone bridge.
Using Kirchhoff’s rules determine the value of unknown resistance R in the circuit so that no current flows through 4 Ω resistance. Also find the potential difference between A and D.
Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would b the potential difference between points B and E?
Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would b the potential difference between points A and B?
In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential at point B.
Consider the circuit shown in the figure. Find (a) the current in the circuit (b) the potential drop across the 5 Ω resistor (c) the potential drop across the 10 Ω resistor (d) Answer the parts (a), (b) and (c) with reference to the figure.
Find the equivalent resistances of the networks shown in the figure between the points a and b.
Two unequal resistances, R1 and R2, are connected across two identical batteries of emf ε and internal resistance r (see the figure). Can the thermal energies developed in R1 and R2 be equal in a given time? If yes, what will be the condition?
On which conservation principle is Kirchoff's Second Law of electrical networks based?
Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit.
Twelve wires each having a resistance of 3 Ω are connected to form a cubical network. A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corners of this network. Determine its equivalent resistance and the current along each edge of the cube.
State Kirchhoff ’s voltage rule.
State the principle of potentiometer.
A copper wire of 10-6 m2 area of cross-section, carries a current of 2 A. If the number of electrons per cubic meter is 8 × 1028, calculate the current density and average drift velocity.
A potentiometer wire has a length of 4 m and resistance of 20 Ω. It is connected in series with resistance of 2980 Ω and a cell of emf 4 V. Calculate the potential along the wire.
In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63 cm, what is the emf of the second cell?
The instrument for the accurate measurement of the e.m.f of a cell is ______.
Kirchhoff’s second law is a consequence of law of conservation of ______.
Figure shows current in a part of an electrical circuit. Then current I is ______.
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
While measuring the length of the rod by vernier callipers, the reading on the main scale is 6.4 cm and the eight divisions on vernier is in line with marking on the main scale division. If the least count of callipers is 0.01 and zero error - 0.04 cm, the length of the rod is ______.
Two cell of 1.25 V and 0.75 V are connected parallel. The effective voltage will be:-
The e.m.f of The battery in a thermocouple is doubled. The rate of heat generated at one of the junction will.
Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio `"i"_3/"i"_1` of currents in terms of resistances used in the circuit is :
Kirchhoff’s junction rule is a reflection of ______.
- conservation of current density vector.
- conservation of charge.
- the fact that the momentum with which a charged particle approaches a junction is unchanged (as a vector) as the charged particle leaves the junction.
- the fact that there is no accumulation of charges at a junction.
What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate `R_(unknown)` by any other method?
What is the advantage of using thick metallic strips to join wires in a potentiometer?
The circuit in figure shows two cells connected in opposition to each other. Cell E1 is of emf 6V and internal resistance 2Ω; the cell E2 is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.
State the two Kirchhoff’s rules used in the analysis of electric circuits and explain them.
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
A 6-volt battery is connected to the terminals of a three-metre-long wire of uniform thickness and resistance of 100 ohms. The difference of potential between two points on the wire separated by a distance of 50 cm will be ______.
In the circuit shown in Figure below, E1 and E2 are batteries having emfs of 25V and 26V. They have an internal resistance of 1 Ω and 5 Ω respectively. Applying Kirchhoff’s laws of electrical networks, calculate the currents I1 and I2.
The figure below shows two batteries, E1 and E2, having emfs of 18V and 10V and internal resistances of 1 Ω and 2 Ω, respectively. W1, W2 and W3 are uniform metallic wires AC, FD and BE having resistances of 8 Ω, 6 Ω and 10 Ω respectively. B and E are midpoints of the wires W1 and W2. Using Kirchhoff's laws of electrical circuits, calculate the current flowing in the wire W3:
