Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
(a) Let the effective resistance of the combination be R. The circuit can be redrawn as shown below.
From the figure,
\[\frac{2R}{R + 2} + 1 = R\]
\[ \Rightarrow 3R + 2 = R^2 + 2R\]
\[ \Rightarrow R^2 - R - 2 = 0\]
\[ \Rightarrow R = \frac{+ 1 + \sqrt{1 + 4 \times 1 \times 2}}{2 \times 1}\]
\[ \Rightarrow R = \frac{+ 1 + \sqrt{9}}{2 . 1} = 2 \Omega\]
(b) Total current sent by the battery
\[= \frac{6}{R} = \frac{6}{2} = 3 A\]
Applying Kirchoff's Law in loop 1, we get:-
\[3 \times 1 + 2i = 6\]
\[ \Rightarrow 2i = 3\]
\[ \Rightarrow i = \frac{3}{2} = 1 . 5 A\]
APPEARS IN
संबंधित प्रश्न
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
State the two Kirchhoff’s rules used in electric networks. How are there rules justified?
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.
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.
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.
On which conservation principle is Kirchoff's Second Law of electrical networks based?
Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit.
State Kirchhoff ’s voltage rule.
State the principle of potentiometer.
State and explain Kirchhoff’s rules.
Explain the determination of unknown resistance using meter bridge.
Kirchhoff’s second law is a consequence of law of conservation of ______.
Kirchhoff s second law is based on the law of conservation of ______
What is the advantage of using thick metallic strips to join wires in a potentiometer?
Why are alloys used for making standard resistance coils?
The value of current in the 6Ω resistance is ______.
In the circuit shown in Figure below, E1 and E2 are batteries having emfs of 25V and 26V. They have an internal resistance of 1 Ω and 5 Ω respectively. Applying Kirchhoff’s laws of electrical networks, calculate the currents I1 and I2.
