Kirchhoff's Rules Class 12 Notes | EduRev

Physics Class 12

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Class 12 : Kirchhoff's Rules Class 12 Notes | EduRev

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(b) The Kirchhoff's Voltage Law

The Kirchhoff's voltage law (KVL) states that the algebraic sum of the potential difference around any closed loop of an electric circuit is zero. The KVL is a statement of conservation of energy. The KVL reflects that electric force is conservative, the work done by a conservative force on a charge taken around a closed path is zero.

Kirchhoff`s Rules Class 12 Notes | EduRev We can move clockwise or anticlockwise, it will make no difference because the overall sum of the potential difference is zero.

Kirchhoff`s Rules Class 12 Notes | EduRev We can start from any point on the loop, we just have to finish at the same point.

Kirchhoff`s Rules Class 12 Notes | EduRev An ideal battery is modelled by an independent voltage source of emf E and an internal resistance r as shown in figure A real battery always absorbs power when there is a current through it, thereby offering resistance to flow of current.

Applying KVL around the single loop in anticlockwise direction, starting from point A, we have

Kirchhoff`s Rules Class 12 Notes | EduRev    Kirchhoff`s Rules Class 12 Notes | EduRev

Hence, Kirchhoff`s Rules Class 12 Notes | EduRev

Ex.15 Find current in the circuit

Kirchhoff`s Rules Class 12 Notes | EduRev

Sol. Therefore, all the elements are connected in series

Therefore, current in all of them will be same

let current = I

Applying kirchhoff' s voltage law in ABCDA loop
Kirchhoff`s Rules Class 12 Notes | EduRev

10 + 4i - 20 + i + 15 + 2i - 30 + 3i = 0

10 i = 25 ⇒ i = 2.5 A

Ex.16 Find the current in each wire applying only kirchhoff voltage law

Kirchhoff`s Rules Class 12 Notes | EduRev

Sol. Applying kirchhoff voltage law in loop ABEFA

i1 + 30 + 2 (i1 + i2) - 10 = 0

3i1 + 2i2 + 20 = 0 ...(i)

Applying kirchhoff voltage law in BCDEB

+30 + 2(i1 + i2) + 50 + 2i2 = 0

4i2 +  2i1 + 80 = 0

2i2 + i1 + 40 = 0 ...(ii)

Solving (i) and (ii)

3[-40 -2i2] + 2i2 + 20 = 0
Kirchhoff`s Rules Class 12 Notes | EduRev

-120 - 4i2 + 20 = 0

i2 = - 25 A

and i1 = 10 A

Therefore, i1  i2 = - 15 A

current in wire AF = 10 A from A to E

current in wire EB = 15 A from B to E

current in wire DE = 25 A from D to C

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