(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.
We can move clockwise or anticlockwise, it will make no difference because the overall sum of the potential difference is zero.
We can start from any point on the loop, we just have to finish at the same point.
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
Ex.15 Find current in the circuit
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
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
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
-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