Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
A battery of 10 V is connected across the diagonally opposite points a and f of the given network. Each side of the cube represents a 3-ohm resistor. Current entrees through the point a and leaves through the point f. Let I current is drawn from the battery and enters through point a, due to the symmetry of cube between point a and f, the current will divide itself into equal parts at each corner of the cube.
As you can see in the figure given below:
If we consider the current path ABGFA, then we can write, VA-B + VB-G + VG-F = V
⇒ `("I"/3 xx"R") + ("I"/6 xx "R") + ("I"/3 xx "R") = ("I" xx "R"_"net")`
⇒ `"R"_"net" = "R"/3 + "R"/6 + "R"/3 = (5"R")/6`
∵ R = 3Ω
⇒ `"R"_"net" = (5xx3)/6 = 2.5 Ω`
Current, `"i" = "V"/"R"_"net" = 10/2.5 = 4 "A"`
⇒ i = 4 A
As i = 4 A, hence current through each side of the cube can be marked. The below figure shows the current through each resistance of the network. i.e. each side of the cube.
APPEARS IN
संबंधित प्रश्न
State the two Kirchhoff’s rules used in electric networks. How are there rules justified?
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?
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/5) Ω?
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.
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?
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.
State the principle of potentiometer.
Obtain the condition for bridge balance in Wheatstone’s bridge.
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?
The instrument for the accurate measurement of the e.m.f of a cell is ______.
Two cell of 1.25 V and 0.75 V are connected parallel. The effective voltage will be:-
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.
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.
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:
