Advertisements
Advertisements
Questions
Obtain the condition for bridge balance in Wheatstone’s bridge.
Obtain the balancing conditions in the case of Wheatstone’s bridge.
Advertisements
Solution 1
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.
Solution 2
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
RELATED QUESTIONS
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?
Determine the current drawn from a 12 V supply with internal resistance 0.5 Ω by the infinite network shown in the figure. Each resistor has 1 Ω 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.
ε1 and ε2 are two batteries having emf of 34V and 10V respectively and internal resistance of 1Ω and 2Ω respectively. They are connected as shown in the figure below. Using Kirchhoff’s Laws of electrical networks, calculate the currents I1 and I2.
State Kirchhoff's rules and explain on what basis they are justified.
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 6 Ω?
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (6/11) Ω?
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?
Consider the following two statements:-
(A) Kirchhoff's junction law follows from conservation of charge.
(B) Kirchhoff's loop law follows from conservative nature of electric field.
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.
An infinite ladder is constructed with 1 Ω and 2 Ω resistors, as shown in the figure. (a) Find the effective resistance between the points A and B. (b) Find the current that passes through the 2 Ω resistor nearest to the battery.
Consider the potentiometer circuit as arranged in the figure. The potentiometer wire is 600 cm long. (a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer? (b) If the jockey touches the wire at a distance of 560 cm from A, what will be the current in the galvanometer?
A capacitor of capacitance 8.0 μF is connected to a battery of emf 6.0 V through a resistance of 24 Ω. Find the current in the circuit (a) just after the connections are made and (b) one time constant after the connections are made.
In the circuit shown in the figure below, E1 and E2 are two cells having emfs 2 V and 3 V respectively, and negligible internal resistance. Applying Kirchhoff’s laws of electrical networks, find the values of currents l1 and I2.
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 current rule.
State the principle of potentiometer.
State and explain Kirchhoff’s rules.
Explain the determination of unknown resistance using meter bridge.
How the emf of two cells are compared using potentiometer?
Lightning is a very good example of a natural current. In typical lightning, there is 109 J energy transfer across the potential difference of 5 × 107 V during a time interval of 0.2 s. Using this information, estimate the following quantities:
- the total amount of charge transferred between cloud and ground
- the current in the lightning bolt
- the power delivered in 0.2 s.
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.
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 ______.
Assertion: Kirchhoff’s junction rule follows from conservation of charge.
Reason: Kirchhoff’s loop rule follows from conservation of momentum.
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 ______.
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?
Why are alloys used for making standard resistance coils?
Power P is to be delivered to a device via transmission cables having resistance RC. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced.
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.
Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively, are connected in parallel with the positive end of 10V battery connected to negative pole of 2V battery (Figure). Find the effective voltage and effective resistance of the combination.
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 ______.
A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is:
