Kirchhoff's first and second laws of electrical circuits are consequences of

Question

In a meter bridge experiment, a resistance of \( 10 \, \Omega \) is balanced by a resistance \( X \) with a balance point at \( 40 \, \mathrm{cm} \). What is the value of \( X \)?

Answer 1

To solve this question, we need to understand Kirchhoff's laws and their relation to the principles of conservation in physics.

Kirchhoff's First Law (Junction Rule): This law states that the total current entering a junction equals the total current leaving the junction. Mathematically, it can be expressed as:

\sum I_{\text{in}} = \sum I_{\text{out}}

This law is a consequence of the conservation of electric charge. Since charge cannot accumulate at a junction, the amount of charge flowing into the junction must equal the amount of charge flowing out.

Kirchhoff's Second Law (Loop Rule): This law states that the sum of the potential differences (voltage) around any closed loop in a circuit is zero. Mathematically, it can be expressed as:

\sum V = 0

This law arises from the conservation of energy. As a charge travels around a loop in a circuit, the total energy it gains and loses (expressed as voltage) balances out to zero.

Given these explanations, Kirchhoff's first law relates to the conservation of electric charge, and Kirchhoff's second law relates to the conservation of energy.

Thus, the correct answer is \text{conservation of electric charge and energy respectively}.

Answer 2