Advertisements
Advertisements
Question
Find the equivalent resistances of the networks shown in the figure between the points a and b.
Solution
(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
RELATED QUESTIONS
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.
ε1 and ε2 are two batteries having emf of 34V and 10V respectively and internal resistance of 1Ω and 2Ω respectively. They are connected as shown in the figure below. Using Kirchhoff’s Laws of electrical networks, calculate the currents I1 and I2.
State Kirchhoff's rules and explain on what basis they are justified.
Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them to get an equivalent resistance of (11/5) Ω?
Determine the equivalent resistance of networks shown in Fig.
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 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.
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.
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 voltage rule.
State the principle of potentiometer.
How the emf of two cells are compared using potentiometer?
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
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 ______.
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.
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.
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.
