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 junction law is equivalent to .............................
(a) conservation of energy.
(b) conservation of charge
(c) conservation of electric potential
(d) conservation of electric flux
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.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/5) 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?
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.
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.
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.
Explain the determination of unknown resistance using meter bridge.
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.
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 ______.
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.
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 value of current in the 6Ω resistance is ______.
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.
