Name: EMF of a Battery
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: Everyone thinks that a battery is a perfect supplier of current, and it does not have internal resistance. But the fact is different. Let us examine this in...

Question

State and explain Kirchhoff's laws for electric circuits. What are the conservation laws implied in each law? State the sign convention for current and emf. Use the given circuit for your explanation.

Accepted Answer

Kirchoff's First law (Kirchoff's current law or KCL): In an electric circuit is stated as the algebraic sum of currents meeting at any junction in the circuit is zero."

Mathematically $\sum_{} I=0$

$\Rightarrow I_{1} + I_{2} + I_{3} = 0$ , Also it can be stated that Total current coming towards the junction is numerical equal to outgoing current from the junction.

Kirchoff's current law is based on the principle of Consecration of charge.

Sign convention for this law is used as the current towards the junction is taken as positive and for current moving away from the junction is taken as negative.

Kerckhoffs Second law(Kirchoff's voltage law or KVL) : In any closed loop of a circuit, Algebraic sum of voltage is equal to algebraic sum of emf of the loop.

Mathematically, $\sum_{} V = 0 \Rightarrow \sum_{} IR= \sum_{} E$

In closed loop ACDBA by using KVL

$\Rightarrow I_{1} R_{1} - I_{2} R_{2} - E_{1} = 0 \Rightarrow I_{1} R_{1} - I_{2} R_{2} = E_{1}$

Similarly, in the closed loop ABEFA by using KVL

$I_{1} R_{2} - I_{2} R_{3} + E_{2} = 0 \Rightarrow I_{1} R_{2} - I_{2} R_{3} = - E_{2}$

Kirchoff's voltage law or KVL is based on the principle of Consecration of Energy.

Sign Connection:

Product of Current and resistance is +ve if we travel in the direction of current and Emf is +ve when we travel from -ve to +ve electrode of a cell through electrolyte.

State and explain Kirchhoff's laws for electric circuits. What are the conservation laws implied in each law? State the sign convention for current and emf. Use the given circuit for your explanation.

Important Questions on DC Circuits and Measurements

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