Question 7: The loop rule is based on the conservation of energy principle and the junction rule on the conservation of charge principle. Explain how these are based on these principles?

ANSWER

Kirchhoff loop rule (second law) states that “In a closed electrical circuit the algebraic sum of all the electromotive forces and the voltage drops in the resistors of the circuit is zero.”

Mathematically,

Here ε is the electromotive force in the circuit, I is the current flowing in the circuit, R is the load and r is the internal resistance of the emf.

Consider this equation. The left side of the equation is the energy gained by a unit charge as it goes through the battery. The right side gives an account of the utilization of that energy; part of the energy gained (Ir), is dissipated into the battery and the rest, IR, in the external circuit. Thus the emf supplies energy to the charge as source of energy and the potential drop across various elements dissipate this energy into other forms of energy.

Kirchhoff junction rule (first law) states “the algebraic sum of all the currents flowing toward a junction is equal to the sum of all the currents flowing away from the junction”.

Mathematically

This indicates the law of conservation of charge.  The net charge at the node is zero. Charge neither accumulates nor produced at the junction. Therefore, charge is conserved.