Advertisements
Advertisements
प्रश्न
Find the equivalent resistances of the networks shown in the figure between the points a and b.
Advertisements
उत्तर
(a) The circuit can be simplified stepwise, as shown below.
The effective resistance between the points a and b,
\[R_{eff} = \frac{\frac{5r}{3} \times r}{\frac{5r}{3} + r} = \frac{5r}{8}\]
(b) The circuit can be simplified, as shown below.
The effective resistance between the points a and b,
\[R_{eff} = \left( \frac{r}{3} \right) + r = \frac{4r}{3}\]
(c)
From the figure, it can be seen that axbya is a balanced Wheatstone bridge. The resistors in branch xy will, thus, become ineffective. The circuit can be simplified as under
The effective resistance between the points a and b,
\[R_{eff} = \left( \frac{2r \times 2r}{2r + 2r} \right) = r\]
(d) The circuit can be simplified as shown below.
The effective resistance between the points a and b,
\[R_{eff} = \frac{r}{4}\]
(e) The circuit can be redrawn as shown below.
Now, we can see that the circuit is a balanced Wheatstone bridge. So, the branch xy will become ineffective. Thus, the simplified circuit will become as shown below.
The effective resistance between the points a and b,
\[R_{eff} = \left( \frac{2r \times 2r}{2r + 2r} \right) = r\]
APPEARS IN
संबंधित प्रश्न
Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.
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.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of 6 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.
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?
Find the circuit in the three resistors shown in the figure.
Twelve wires, each of equal resistance r, are joined to form a cube, as shown in the figure. Find the equivalent resistance between the diagonally-opposite points a and f.
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?
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.
How the emf of two cells are compared using potentiometer?
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 ______.
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 ______.
The e.m.f of The battery in a thermocouple is doubled. The rate of heat generated at one of the junction will.
The figure below shows current in a part of electric circuit. The current I is ______.
Kirchhoff s second law is based on the law of conservation of ______
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.
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?
What is the advantage of using thick metallic strips to join wires in a potentiometer?
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
The value of current in the 6Ω resistance is ______.
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:
