Advertisements
Advertisements
Question
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
Advertisements
Solution
In this case, Kirchhoff’s junction rule applied to junctions D and B (see the figure) immediately gives us the relations I1 = I3 and I2 = I4. Next, we apply Kirchhoff’s loop rule to closed loops ADBA and CBDC.
The first loop gives
–I1R1 + 0 + I2R1 = 0 ...(Ig = 0)
And the second loop gives, upon using I3 = I1, I4 = I2
I2R4 + 0 – I1R3 = 0
From the equation, we obtain,
`I_1/I_2 = R_2/R_1`
Whereas from the equation, we obtain,
`I_1/I_2 = R_4/R_3`
Hence, we obtain the condition
`R_2/R_1 = R_4/R_3`
This last equation relating the four resistors is called the balance condition for the galvanometer to give zero or null deflection.
The Wheatstone bridge and its balance condition provide a practical method for the determination of unknown resistance. Let us suppose we have an unknown resistance, which we insert in the fourth arm; R4 is thus not known. Keeping known resistances R1 and R2 in the first and second arm of the bridge, we go on varying R3 till the galvanometer shows a null deflection. The bridge then is balanced, and from the balance condition the value of the unknown resistance R4 is given by, R4 = `R_3 R_2/R_1`
APPEARS IN
RELATED QUESTIONS
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.
Determine the equivalent resistance of networks shown in Fig.
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.
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?
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.
How the emf of two cells are compared using potentiometer?
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?
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.
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.
In a meter bridge the point D is a neutral point (Figure).
- The meter bridge can have no other neutral point for this set of resistances.
- When the jockey contacts a point on meter wire left of D, current flows to B from the wire.
- When the jockey contacts a point on the meter wire to the right of D, current flows from B to the wire through galvanometer.
- When R is increased, the neutral point shifts to left.
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?
