Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 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 (6/11) 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.
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?
In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential at point B.
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.
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.
Figure shows current in a part of an electrical circuit. Then current I is ______.
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
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?
State the two Kirchhoff’s rules used in the analysis of electric circuits and explain them.
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
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 ______.
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:
