Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Kirchhoff’s First Law − Junction Rule
The algebraic sum of the currents meeting at a point in an electrical circuit is always zero.
Let the currents be I1, I2I3, and I4
Convention:
Current towards the junction − positive
Current away from the junction − negative
I3 + (− I1) + (− I2) + (− I4) = 0
Kirchhoff’s Second Law − Loop Rule
In a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the products of the resistances and current flowing through them.
For closed part BACB, E1 − E2 = I1R1 + I2 R2 − I3R3
For closed part CADC, E2 = I3R3 + I4R4 + I5R5
Wheatstone Bridge:
The Wheatstone Bridge is an arrangement of four resistances as shown in the following figure.
R1, R2, R3,and R4 are the four resistances.
Galvanometer (G) has a current Ig flowing through it at balanced condition, Ig = 0
Applying junction rule at B,
∴ I2 = I4
Applying junction rule at D,
∴ I1 = I3
Applying loop rule to closed loop ADBA,
`-I_1R_1+0+I_2R_2 = 0`
`∴ I_1/I_2 = R_2/R_1 ...... (1)`
Applying loop rule to closed loop CBDC,
`I_2R_4+0-I_1R_3 = 0` ∵`I_3 =I_1,I_4 =I_2`
`∴ I_1/I_2 = R_4/R_3 ...... (2)`
From equations (1) and (2),
`R_2/R_1 = R_4/R_3`
This is the required balanced condition of Wheatstone Bridge.
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
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 the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of 6 Ω?
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.
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.
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.
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?
State Kirchhoff ’s voltage rule.
The e.m.f of The battery in a thermocouple is doubled. The rate of heat generated at one of the junction will.
Kirchhoff s second law is based on the law of conservation of ______
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 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:
