Question

Kirchhoff’s first law is given by $ \sum I = 0 $ and Kirchhoff’s second law is given by $ \sum I R = 0 $ , where the symbols have their usual meanings. Choose the correct option.
(A) Kirchhoff’s first law is based on conservation of energy and second law is based on conservation of charge.
(B) Kirchhoff’s second law is based on the conservation of energy and the first law is based on conservation of charge.
(C) Both the laws based on the conservation of momentum.
(D) First law based on the conservation of momentum and second law on the conservation of charge.

Answer 1

Hint: To solve this type of problem we should know about the basics of Kirchhoff’s law. This law is given by a German physicist Gustav Kirchhoff. Kirchhoff’s circuit laws are two equalities which deal with current and potential differences in the element model of electric circuits. It quantifies how current flows through a circuit and how voltage will vary around a loop in the circuit.

Complete step by step solution:
To solve this first we understand the statement of Kirchhoff’s laws:
Kirchhoff’s first law: this is based on the law of conservation of charge. It states that at any circuit junction the sum of current flowing into and out of that junction are equal. In simple words we can say the sum of all current entering a point will be equal to sum of all currents leaving the point.
Mathematically, we can say that:
  $ \sum\limits_{k = 1}^n {{I_k} = 0} $
Here $ n $ is the total number of branches carrying current towards or away from a given node.
Kirchhoff’s second law: this law is based on conservation of energy around a closed path. It states that for a closed loop series the algebraic sum of all the voltage around a closed loop in any circuit must be equal to zero. In simple words the algebraic sum of voltage along all battery and voltage drop around each element present in circuit will be zero.
  $ \sum V = 0 $
So, from above we can conclude that Kirchhoff’s second law is based on the conservation of energy and the first law is based on conservation of charge.
Hence (b) will be the correct option.

Note:
They are used to analyze any electric circuit and computation of current and voltage of complex circuits. There are advantages like it is easier to calculate unknown current and voltage in a complex circuit. There are limitations of Kirchhoff’s law that is it works under the assumption that there is no fluctuating magnetic field in the closed loop. Electric field and emf could be induced which cause the Kirchhoff’s loop rules to break in presence of a variable of a variable magnetic field.