Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let V be the potential difference between the points a and f. Let current i enter a and leave from f. The distribution of current in various branches is shown in figure.
To calculate the potential difference between a and f, consider the path abcf and apply Kirchofff's Law:-
\[\frac{i}{3}r + \frac{i}{6}r + \frac{i}{3}r = V\]
\[\Rightarrow \left( \frac{2ir}{3} + \frac{ir}{6} \right) = V\]
\[ \Rightarrow \left( \frac{5ir}{6} \right) = V\]
The effective resistance between a and f,
\[R_{eff} = \frac{V}{i} = \frac{5}{6}r\]
APPEARS IN
संबंधित प्रश्न
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?
The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for
- the current draw from the cell and
- the power consumed in the network.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of 6 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?
Determine the equivalent resistance of networks shown in Fig.
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.
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 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.
State Kirchhoff’s current rule.
Explain the determination of unknown resistance using meter bridge.
Kirchhoff’s second law is a consequence of law of conservation of ______.
Assertion: Kirchhoff’s junction rule follows from conservation of charge.
Reason: Kirchhoff’s loop rule follows from conservation of momentum.
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 :
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.
