Kirchoff’s Voltage law

Kirchoff’s voltage law is about the EMF and voltage in a closed circuit or a closed loop and may be stated as under

“In any closed electrical circuit the algebraic sum of all the electromotive force(e.m.f) and voltage drop in a resistor is equal to zero i-e.

Algebraic sum of emf + algebraic sum of voltage drops = zero

Kirchoff's Voltage law

The validity of kirchoff’s Voltage law can be easily established by referring to the closed loop ABCDA which is shown in the figure.

Starting from any point(Say point A) in this closed circuit and go back to this point(i-e point A) after going around the circuit, then there is no increase or decrease in potential.

During Considering the circuit shown in the figure the following convention is adopted to solve the electrical circuit.

  • A rise in potential is taken positive
  • A drop in potential is taken negative
  • For batteries the positive and is always at Higher potential
  • Current flow from high potential to low potential
  • Assume the direction of current either clockwise or counterclockwise
Kirchoff's Voltage law

Let’s take counter clockwise around.Considered current from positive terminal of emf ɛ1 we take the rise of potential as + ɛ1,through R1 ,the voltage drops s –IR1,Across ɛ2 from the +ve  to –ve sde there is a fall of potential – ɛ2.Through R2, there is a voltage drop of –IR2,apply Kirchoff’s law of voltage (KVL) ,we get

ɛ1-IR1– ɛ2-IR2=0

ɛ1– ɛ2=IR1-IR2

∑ɛ =∑IR

The sum of all the emf ɛ in a loop in a circuit is equal to the sum of all the IR voltage drops in that loop.KVL is in fact,a statement of the law of conservation of energy.

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