Advertisements
Advertisements
Question
The circuit in figure shows two cells connected in opposition to each other. Cell E1 is of emf 6V and internal resistance 2Ω; the cell E2 is of emf 4V and internal resistance 8Ω. Find the potential difference between the points A and B.
Advertisements
Solution
In this problem, after finding the electric current flow in the circuit by using Kirchoff’s law or Ohm’s law, the potential difference across AB can be obtained.
Applying Ohm's law.
Equivalent emf of two cells = 6 – 4 = 2V and equivalent resistance = 2Ω + 8Ω = 10Ω, so the electric current is given by
`I = (6 - 4)/(2 + 8)` = 0.2 A
Taking loop in anti-clockwise direction, since E1 > E2
The direction of flow of current is always from high potential to low potential.
Therefore VB > VA.
⇒ VB – 4V – (0.2) × = VA
Therefore, VB – VA = 3.6V
Important point: Sign convention for the application of Kirchoff’s law: For the application of Kirchoff’s laws following sign convention are to be considered.
(i) The change in potential in traversing a resistance in the direction of current is – iR while in the opposite direction + iR.
(ii) The change in potential in traversing as emf source from negative to positive terminal is +E while in the opposite direction – E irrespective of the direction of current in the circuit.
APPEARS IN
RELATED QUESTIONS
Kirchhoff's voltage law and current law are respectively in accordance with the conservation of .................................. .
- charge and momentum
- charge and energy
- energy and charge
- energy and momentum
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?
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.
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.
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.
State Kirchhoff's rules for an electric network. Using Kirchhoff's rules, obtain the balance condition in terms of the resistances of four arms of Wheatstone bridge.
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 B and E?
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.
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.
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 current rule.
State Kirchhoff ’s voltage rule.
Lightning is a very good example of a natural current. In typical lightning, there is 109 J energy transfer across the potential difference of 5 × 107 V during a time interval of 0.2 s. Using this information, estimate the following quantities:
- the total amount of charge transferred between cloud and ground
- the current in the lightning bolt
- the power delivered in 0.2 s.
A potentiometer wire has a length of 4 m and resistance of 20 Ω. It is connected in series with resistance of 2980 Ω and a cell of emf 4 V. Calculate the potential along the wire.
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?
Assertion: Kirchhoff’s junction rule follows from conservation of charge.
Reason: Kirchhoff’s loop rule follows from conservation of momentum.
The Kirchhoff's second law (ΣiR = ΣE), where the symbols have their usual meanings, is based on ______.
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 ______.
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 :
What is the advantage of using thick metallic strips to join wires in a potentiometer?
Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.
The figure below shows two batteries, E1 and E2, having emfs of 18V and 10V and internal resistances of 1 Ω and 2 Ω, respectively. W1, W2 and W3 are uniform metallic wires AC, FD and BE having resistances of 8 Ω, 6 Ω and 10 Ω respectively. B and E are midpoints of the wires W1 and W2. Using Kirchhoff's laws of electrical circuits, calculate the current flowing in the wire W3:
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:
